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tee on  the  Library.  i 


Digitized  by  the  Internet  Archive 
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https://archive.org/details/practicalcottonsOOscot_0 


» 


t 


THE  PRACTICAL 

COTTON  SPINNER, 

AND 

MANUFACTURER. 


THE  PRACTICAL  V- 

COTTON  SPINNE 

AND 

MANUFACTURER: 

THE 

MANAGERS',  OVERLOOKERS',  AND  MECHANICS' 
COMPANION. 

A  COMPREHENSIVE  SYSTEM  OF 

CALCULATIONS  OF  fflLL  GEARING  AND  MACHINERY, 

FROM  THE  PEIMAEY  MOVING  POWEK,  THROUGH  THE  DIFFERENT  PROCESSES  OF 

CARDING,  DRAWING,  SLUBBING,  ROVING,  SPINNING,  AND  WEAVING, 
With  the  recent  improvements  in  Machinery. 

TO  WHICH  ARE  ADDED, 

Compendious  Tables  of  Yarns  and  Heeds  for  Silk,  Linen,  Worsted,  and  Wool. 
BY  R.  SCOTT. 

Comctiti  anJj  jHnlarstU,  toitlj  ^3Iatcs  of  Hmcrtcait  <l'laci)iitcs, 
BY  OLIVER  BYRNE, 

CiyiL,  MILITARY,  AND  MECHANICAL  ENGINEER  ; 

COMPILER  AND  EDITOR  OF  THE  "  DICTIONARY  OF  MACHINES,  MECHANICS,  ENGINE-WORK,  AND 
ENGINEERING         AUTHOR  OF  "  THE  PRACTICAL  MODEL  CALCULATOR,''  AUTHOR  OF  "  THE 
COMPANION  FOR  MACHl  NISTS ,  MECHANICS,  AND  ENGINEERS  ;  "  AUTHOR  AND  INVENTOR 
OF  A  NEW  SCIENCE,  TERMED       THE  CALCULUS  OF  FORM,"  A  SUBSTITUTE  FOR 
THE  DIFFERENTIAL  AND  INTEGRAL  CALCULUS;   AND  NUVIEROUS  OTHER 
MATHEMATICAL  AND  MECHANICAL  WORKS,  ETC.  ETC.  ETC. 


PHILADELPHIA: 
HENRY    CAREY  BAIRD, 

SUCCESSOR  TO  E.  L.  CAREY. 

1851. 


Entered  according  to  the  Act  of  Congress,  in  the  year  1851,  by 

HENRY  CAREY  BAIRD, 

Office  of  the  Clerk  of  the  District  Court  in  and  for  the  Eastern  District  of 
Pennsylvania. 


PHILADELPHIA  : 
T.  IC.  AND  P.  G.  COLLINS,  PRINTERS. 


PEEF  ACE. 


Several  publications  on  Cotton  Spinning  have  appeared,  the 
merits  of  "which  it  is  not  my  intention  to  discuss.  As  a  practical 
■working  man,  I  may  however  observe,  that  those  which  have 
come  under  my  notice  are,  to  a  considerable  extent,  destitute  of 
much  practical  utility.  The  systems  they  contain  of  making  the 
calculations,  are  not  sufficiently  explicit,  and  hence  can  never 
achieve  the  great  and  important  object  of  combining  practice 
with  theory,  which  is  so  essential,  particularly  to  managers  and 
overlookers. 

The  present  work  contains  every  necessary  calculation  con- 
nected with  the  most  recent  improvements  in  the  machinery  em- 
ployed in  the  spinning  and  manufacturing  business.  The  rules, 
examples,  and  illustrations  are  simple  and  easily  understood ; 
so  much  so  that  any  person  having  a  knowledge  of  the  element- 
ary rules  of  arithmetic  may,  without  difficulty,  by  a  little  atten- 
tion to  the  rules  and  examples,  prepare  himself  to  fill  the  impor- 
tant situation  of  overlooker  or  manager  in  any  department  of 
the  spinning  and  manufacturing  business.  The  rules  and  exam- 
ples are  all  original,  and  have  been  reduced  to  practice  with 
great  care. 

Calculations  relative  to  the  machinery  used  in  the  spinning  and 
manufacturing  of  all  fibrous  substances,  are  attainable  by  the 
rules  established  in  this  work,  so  that  it  will  be  found  equally 
beneficial  to  those  engaged  in  the  spinning  and  manufacturing  of 
silk,  flax,  worsted,  and  wool.  Compendious  tables  are  arranged, 
accompanied  with  rules,  examples,  and  illustrations,  to  show  the 
size,  girt,  hank,  or  proportion  of  hank,  in  every  operation.  The 


\  ^  ^  ^ 


vi 


PREFACE. 


fineness  of  yarns  according  to  the  different  lengths,  constituting 
the  lea,  cut,  or  hank,  with  the  different  systems  of  counting 
worsted  reeds,  are  added. 

During  my  engagements  for  many  years  in  the  different  de- 
partments of  the  cotton  business,  I  found  a  great  deficiency  of 
theoretical  knowledge  among  practical  persons  filling  important 
situations  in  cotton  and  other  factories.  This  led  to  the  deter- 
mination, at  the  request  and  by  the  encouragement  of  several 
friends,  to  prepare  a  complete  system  of  calculations;  and  I  have 
no  hesitation  in  saying,  that  such  a  system  will  be  found  in  the 
present  work.  And  while  it  answers  as  a  book  of  reference  to 
the  master,  and  an  assistant  to  the  manager,  overlooker,  and 
mechanic,  it  will  convey  instructions  to  the  aspiring  operative, 
and  may  be  found  a  useful  auxiliary  in  the  tuition  of  young  per- 
sons intended  for  the  spinning,  manufacturing,  or  machine  busi- 
ness. This  work  will  not  only  be  found  to  convey  a  correct 
knowledge  of  its  appropriate  calculations,  but,  in  following  out 
the  rules  here  laid  down,  a  considerable  degree  of  pleasure  must 
be  experienced  when  it  is  found  that  theory  and  practice  are  so 
beautifully  combined,  and  that  it  will  enable  persons  to  give 
general  satisfaction  in  the  management  of  their  respective  de- 
partments of  this  peculiarly  important  business. 

It  has  been  remarked,  that  "the  country  which  parts  with  the 
raw  materials  of  labor,  is  afterwards  bereft  of  the  sustenance  of 
man — food  goes  away  to  visit  industry,  and  hunger  remains  to 
dwell  with  idleness,  and  famine  descends,  Avith  all  its  terrors,  to 
castigate  the  folly  which  blindly  relinquishes  the  material  of 
manufactures." 

Foreign  manufactures  are  the  destruction  of  any  country ; 
and  we  believe,  the  people  may  stop  or  retard  that  destruction 
by  superseding  such  manufactures,  by  producing  articles  equally 
good  and  cheap.  A  divided  people,  it  is  manifest,  cannot  pur- 
chase victory  in  war  ;  the  industrial  prosperity  of  peace  is  equally 
impossible  to  a  people  who  are  at  war  with  each  other.  Besides — 
let  us  not  blink  the  truth — the  nations  that  have  distinguished 
themselves  in  industry  and  commerce,  had  always  first  distin- 


PREFACE. 


vii 


guished  themselves  in  arms  for  freedom.  When  the  Persian 
was  chased  from  the  shores  of  Greece  like  a  wolf,  the  republican 
Greek  became  a  great  trader. 

The  Saracens'  conquests  gave  place  to  their  commerce  ;  after 
the  scimitar  came  the  shuttle.  The  Dutch  laid  down  the  arque- 
buse  to  assume  the  tiller.  The  Italians  of  their  republican  ages 
relieved  guard  alternately  at  the  rich  loom  and  the  Goth-defying 
bastion. 

However,  it  requires  not  a  prophet's  inspiration  to  foretell  that 
the  day  is  fast  approaching  when  none  but  the  superabundant  raM" 
material  will  be  shipped  from  this  country.  The  South  and  West 
have  made  more  than  a  beginning  in  manufacturing  their  own 
cotton,  iron,  hemp,  flax,  &c.,  and  the  North  and  East  can  more 
than  vie  with  Europe  in  wonder-working  machinery.  I  have 
held  these  opinions  for  some  time,  and  am  much  strengthened  in 
them,  on  reviewing  the  vast  improvements  introduced  into  the 
cotton  manufacturing  business  by  American  machinists  and  engi- 
neers. I  may  particularize  the  Niagara  Throstle,  or  McCuUey's 
patented  improved  Spinning  Frame  ;  Mason's  Self-acting  Mule ; 
Judkin's  Heddle  Machine.  Respecting  these  machines  we  have 
entered  into  particulars,  and  have  given  large  working  drawings 
of  them. 

I  should  have  mentioned  the  Cop-spinner  of  Dodge  and  Sons, 
of  Dodgeville,  Attleborough,  Massachusetts.  This  first  class 
machine  will  wind  the  yarn  as  fast  as  twisted,  or  when  properly 
twisted,  upon  each  of  the  spindles  in  a  regular  or  proper  shaped 
cop,  which  shall  have  a  binding  thread  between  each  two  adja- 
cent layers  of  yarn,  which  prevents  the  cop  from  falling  apart 
while  being  removed  from  the  spindle. 


CONTENTS. 


MILL  GEARING,  &c. 

Page 


Revolutions  of  Shaft  a  minute            ....  9 

Revolutions  of  Beater  at  Blowing  Machine  a  minute    .          .  22 

Revolutions  of  main  Cylinder  of  Carding  Engine         .          .  23 

Revolutions  of  Counter  Shaft  a  minute           ...  24 

ON  MIXING  COTTON. 
Observations  ou         ......  25 

ON  MACHINERY. 

Observations  and  Rules  for  working  Speeds,  &c  .  .  26 

Willow,  Particulars  of  .  .  .  .  .26 

Blowing  Machine       ......  27 

Dimensions  of  a  double  Blowing  JIachine,  including  speeds,  tra- 
versing of  Rollers,  &c.        .  .  .  .  .35 

Lap  Machine  .  .  .  .  .  .35 

Particulars  of  Lap  Machine,  including  speeds,  intermediate 

draughts,  total  draughts,  &c.  ....  48 

Carding  Engine,  Observations  on        .  .  .  .48 

Speeds,  intermediate  draughts,  total  draught,  consumption,  pro- 
duction, &c.  ......  49 

Particulars  of  a  Carding  Engine         ....  70 

Drawing  Frame,  speeds,  intermediate  draughts,  total  draughts, 
consumption  and  production  at  each  head,  weight  of  Cotton, 
and  length  of  Carding  required  to  supply  the  first  head  of 
drawing,  &c.  ......  71 

1 


X 


CONTENTS. 


Particulars  of  Drawing  Frame  .... 

Page 
91 

Tube  Frame,  Observations  on  .... 

92 

Speeds,  intermediate  draughts,  total  draught,  consumption,  pro- 

duction, &c.  ...... 

92 

Particulars  of  a  Tube  Frame  ..... 

110 

Slubbing  Frame,  speeds,  intermediate  draughts,  total  draught. 

consumption  and  production,  turns  per  inch,  size,  girt,  or 

hank  of  slubbing,  &c.         .  .  .  .  .111 

Roving  Frame,  speeds,  intermediate,  draughts,  total  draught, 
consumption  of  slubbing,  production  of  roving,  size,  girt,  or 
hank  roving,  loss  sustained  in  working,  turns  per  inch,  &c.    .  123 
Throstles,  Observations  on      .  .  .  .  .132 

Speeds,  intermediate  draughts,  total  draught,  production,  &c.    .  133 
Particulars  of  Throstle  .....  143 

Mules,  speeds,  intermediate  draughts,  total  draught,  gain  at 
carriage,  consumption  of  Roving,  production  of  Yarn,  turns 
per  inch,  &c.  .....  .  144 

Tables,  showing  the  Weight  of  Carding  and  Drawing,  according 
to  the  length,  weight,  and  size  or  girt  in  each  operation,  with 
rules  and  examples  .....  164 

Table,  showing  the  dividend  for  any  number  of  inches  from  1  to 
36,  whereby  the  Weight  of  Cotton  required  to  be  fed  on  the 
Feed  Cloth  at  the  Lap  Machine  may  be  ascertained  for  any 
numbers  of  Yarn,  according  to  the  proportion  of  the  hank  at 
the  Lap  Machine,  with  rules  and  examples   .  .  .177 

Tables  of  Carding,  Drawing,  Slubbing  and  Roving,  with  rules 

and  examples;  Change  Wheels,  &c.  .  .  .  178 

Self-acting  Mule,  revolutions  of  all  the  different  movements  per 
minute,  intermediate  draughts,  total  draught,  traverses,  pro- 
duction, turns  per  inch,  &c.  &c.      ....  192 

Particulars  of  the  Self-acting  Mule,  with  observations,  &c.        .  228 
Hank  or  proportion  of  Hank  in  each  and  every  operation  from 

the  Spinning  to  the  Lap  Machine    ....  230 

Loss  in  working  Cotton  .....  235 

Table  of  multipliers  for  ascertaining  the  loss  sustained  in  work- 
ing any  given  length,  or  weight  of  Cotton,  &c.        .  .  244 


CONTENTS.  xi 

Page 

Loss  in  working  any  given  length,  or  weight    .          .           .  246 

Average  Cop  and  weight  of  Sets         ....  247 

Spinner's  Book,  &c.    .          .          .          .          .          .  255 

Dressing  Machine,  speed,  &c.             ....  257 

Particulars  of  Dressing  Frame            ....  262 

Power  Loom,  speeds,  weight  of  Yarn  required  for  a  piece  of 

Cloth,  &c.  .......  263 

Wheels  required  to  produce  any  given  draught,  &c.      .          .  271 
Wheels  required  to  produce  any  given  draught,  &c.,  by  cancel- 
ling          .......  282 

Reed  Tables,  explanation       .....  293 

Reed  Tables,  different  systems  of  counting  Reeds  brought  into 

conjunction  with  each  other,  with  rules  and  examples          .  295 
Manufacturing  of  Cotton,  Silk,  &c.,  weight  of  Warps  and  Weft 

required  for  any  fabric  of  Cloth       ....  306 

Linen  Yarn  Tables,  different  Reels      ....  336 

Linen  Yarn  Tables,  showing  the  weight  according  to  the  num- 
bers or  fineness  of  Yarns,  and  the  different  lengths  weighed, 

with  rules  and  examples      .....  337 

Linen  manufacture.  Yarns  required  to  produce  any  fabric  of 

Cloth        .......  364 

Worsted  and  Woollen  Yarns,  Observations  on,  with  explanation 

to  the  Yarn  Table  ......  367 

Tables  of  Worsted  and  Woollen  Yarns,  showing  the  weight  of 
one  hank,  dozen,  and  gross,  according  to  the  fineness,  with 
rules  and  examples  for  ascertaining  the  length  and  weight 

of  Yarns  for  any  fabric  of  Cloth,  &c.          .           .          .  368 

Worsted  Count  of  Reeds,  Observations  on,  and  explanation  of 

Reed  Tables          ......  380 

Worsted  Reed  Table,  with  rules,  examples,  &c.           .          .  381 

Miscellaneous  Questions  and  Examples           .          .          .  386 
Rule  and  Examples  for  changiag  light  Gearing  to  heavy,  or 

heavy  Gearing  to  light       .....  396 

C.  J.  Judkins'  American  Healds,  or  Heddles  .          .          .  398 

Mason's  Self  acting  Mule       .....  399 

Niagara  Throstle  or  McCulley's  Spinning  Frame  .  .  416 
Plates  I.  IL  III.  IV.  V.  VI.  VII.  VIII.        .          .  .416 


THE 

PEACTICAL  COTTON  SPINNER 

AND 

MANUFACTURER. 


MILL  GEERING. 

Opinions  relative  to  the  best  speeds  for  machinery  may  differ ; 
however,  the  following  speeds  are  such  as  are  generally  adapted 
to  machines  spinning  medium  numbers  ;  but  all  machinery  must 
be  speeded  according  to  the  quantity  required. 

RULES  FOR  WORKING  SPEEDS  OF  SHAFTS. 

Multiply  the  strokes  of  the  steam  engine,  or  revolutions  of  the 
waterwheel,  by  the  number  of  teeth  in  the  wheel  fixed  on  the 
first  moving  power,  or  given  shaft,  for  a  dividend,  and  divide  by 
the  number  of  teeth  in  the  wheel  fixed  on  the  intended  driven 
shaft,  and  the  quotient  will  be  the  speed  or  revolutions  of  shaft 
required. 

To  find  the  speed  of  any  given  shaft,  when  the  speeds  of  the 
intermediate  shafts  are  not  required. 

Multiply  all  the  driving  wheels  together  respectively,  so  far  as 
the  shaft  you  want  the  speed  of,  and  that  product  by  the  strokes 
of  the  engine,  the  revolutions  of  the  waterwheel,  or  any  shaft: 
the  speed  being  known  for  a  dividend,  then  multiply  all  the 
driven  wheels  together  accordingly,  for  a  divisor,  and  the  quo- 
tient will  be  the  speed,  or  revolutions  of  the  shaft  required. 

If  a  steam-engine  makes  22  double  strokes  a  minute  (that  is 
the  same  as  to  make  the  crank  revolve  22  times  a  minute)  with 
a  wheel  fixed  on  the  crank,  or  fly-shaft,  containing  106  teeth ; 
what  revolutions  will  the  first  or  main  line  of  shafts  make,  if  the 
wheel  with  106  teeth  works  into  a  wheel  on  the  first  or  main  line 
of  shafts  with  47  teeth  ? 
2 


10 


SPEED  OF  SHAFTS. 


22  strokes  or  revolutions  each  minute. 
106  teeth  in  wheel  of  crank  or  fly-shaft. 


132 
220 


Teeth  of  wheel  on  J  47)2332(49.617  revolutions  a  minute  of  first 
mam  line  of  shait  S      100  •   r      c  i, 

188  or  main  line  01  shafts. 

452 
423 


290 
282 


80 
4T 


330 

329 


1 

If  a  wheel  with  61  teeth  be  fixed  on  the  first  or  main  line  of 
shafts,  which  makes  49.617  revolutions  a  minute;  what  revolu- 
tions a  minute  will  a  cross-shaft  make  with  a  wheel  57  teeth 
fixed  on  it,  worked  by  the  wheel  with  61  teeth? 

49.617  revolutions  of  shaft  a  minute. 
61  teeth  in  wheel  or  shaft. 


49617 
297702 


Teeth  of  wheel  on  )  57)3026.637(53.098894  revolutions  of  cross- 

cross-snatt          )      ^85  shaft  a  minute,  or 

  510        53.1— nearly. 

176  456 

171   

  540 

563  513 


513 

50 
456 


  270 

507  228 


SPEED  OF  SHAFTS. 


11 


If  a  wheel  with  75  teeth  be  fixed  on  a  shaft  revolving  49.617 
times  a  minute,  works  into  a  wheel  with  41  teeth,  fixed  on  a 
shaft  for  driving  looms  ;  what  number  of  revolutions  will  it  make 
a  minute  ? 

49.617  revolutions  of  shaft  a  min. 
75 


248085 
347319 


41)3721.275(90.7628  revolutions  a  min- 
369  ute  of  shaft  driving 

  looms. 

312 
287 


257 
246 


115 

82 


330 
328 


2 

If  a  wheel  with  52  teeth  be  fixed  on  a  shaft  making  90.7626 
revolutions  a  minute,  works  into  a  wheel  with  41  teeth,  on  the 
foot  of  an  upright-shaft  for  driving  mules;  what  revolutions  a 
minute  will  the  upright-shaft  make? 

90.7628  revolutions  of  shaft  a  minute. 
52  teeth  of  wheel  on  shaft. 


1815256 
4538140 


Teeth  of  wheel  on  shaft 
for  driving  looms 


47196656 


12 


SPEED  OP  SHAFTS. 


Teeth  of  wheel  on~) 

foot  of  upright- y  41)47196656(115.1138  revolutions  a  minute 
shaft,  j      41  of  upright-shaft,  driv- 


61 
41 

209 
205 

46 
41 

56 
41 


ing  mules. 


155 
123 


326 

328— nearly. 

If  a  drum,  20  inches  diameter,  be  fixed  on  an  upright-shaft, 
for  driving  mules,  which  makes  115.1138  revolutions  a  minute; 
what  revolutions  will  the  upright-shaft  in  wheelhouse  for  driving 
rim  or  fly-shaft  make,  if  a  pulley,  12  inches  in  diameter,  be  fixed 
on  a  shaft,  and  worked  by  a  strap  from  the  drum  20  inches  di- 
ameter ? 

115,1138  revolutions  a  minute,  upright-shaft. 
Inches    diam  ^  inches  diameter  of  drum  on  shaft, 

of 

Uprigut-oiiaiL  I 

in  wheelhouse,  J 


}  12)2302.2760 
sht-shaft  ( 


191.8563  revolutions  of  upright-shaft  a 
minute  in  wheelhouse,  for  driv- 
ing rim-shaft. 

If  a  wheel  with  61  teeth  be  fixed  on  the  first  or  main  line  of 
shafts,  making  49.617  revolutions  a  minute ;  what  number  of 
revolutions  will  an  upright-shaft  make,  with  a  wheel  57  teeth 
fixed  on  it,  worked  by  the  wheel  of  61  teeth? 


SPEED  OF  SHAFTS. 


13 


Teeth  in  wheel  on^ 
main-shaft  working 
into  wheel  on  foot  of 
upright-shaft, 


49.617  revol.  a  min.  of  main-shaft. 
.  .  61 


49617 
297702 


a  mm- 


Teeth  of  wheel  on  foot  1      3^26637(53,098894  revols. 

of  upright-shaft,       /    ^285  ute  of  upright- 

  shafts. 

176 
171 


563 
513 


507 

456 


510 
456 


540 
513 


270 
228 


42 


If  a  wheel  with  70  teeth  be  fixed  on  the  top  of  an  upright- 
shaft  making  53.098894  revolutions  a  minute,  and  works  into  a 
wheel  with  39  teeth  on  a  lying-shaft;  what  revolutions  will  the 
lying-shaft  make  a  minute? 

53.098894  revols.  of  upright-shaft  a  minute. 
70  teeth  in  wheel  on  upright-shaft. 


3716.922580 


14 


SPEED  OF  SHAFTS. 


Teeth  of) 

wheel  on  ly-V   39)3716.922580(95.3057  revolutions  of  lying- 


206 
195 


119 
117 


222 
195 


275 
273 


If  a  drum  30  inches  diameter  be  fixed  on  a  shaft  making 
95.3057  revolutions  a  minute ;  what  number  of  revolutions  a 
minute  will  a  shaft  make  with  a  drum  fixed  on  it  18  inches  dia- 
meter, worked  by  a  strap  from  the  drum  30  inches  diameter? 


95.3057  revolutions  of  shaft  a  minute. 
30  inches  diam.  of  drum. 


i.8428  revolutions  of  shaft  a 


105 

90 


159 
144 


151 
144 


77 
72 


ing-shaft, 


351 


shaft  the  minute. 


minute. 


51 
36 


150 
144 


6 


SPEED  OP  SHAFTS. 


15 


If  a  drum  45J  inches  diameter  be  fixed  on  a  shaft  making 
95.30558  revolutions  a  minute;  what  number  of  revolutions  a 
minute  will  a  shaft  make  with  a  pulley  fixed  on  it  13f  inches 
diameter,  and  driven  by  a  strap  from  the  drum  45J  inches  dia- 
meter ? 

95.30558  revolutions  of  shaft. 
45.5  diameter  of  drum. 


47652790 
47652790 
38122232 


Inches 
of 


'\?r°^'  I  13.75)4336.403890(315.3748  revols.  of  counter- 
J  4125  shafts  a  minute, 

  driving  blowing 

2114  and  lap  machines. 

1375 


7390 
6875 

5153 
4125 

10288 
9625 

6639 
5500 

11390 
11000 

390 

If  a  drum  86  inches  diameter  be  fixed  on  a  shaft  making 
315.3748  revolutions  a  minute ;  what  number  of  revolutions  will 
the  beaters  of  a  blowing  machine  make,  if  a  pulley  6  inches 
diameter  be  fixed  on  the  end  of  the  beaters,  and  driven  by  a 
strap  from  the  drum  36  inches  diameter? 


16 


SPEED  OF  SHAFTS. 


315.3748  revolutions  of  counter-shaft  a  minute. 
36  inches  diameter  of  drum  on  shaft. 


18922488 

9461244 

Diam.  of  pul- ")  

ley  on  beat-  V 113534928 
ers,  6  inches,  j  

1892.2488  revolutions  of  beaters  a  minute. 

If  a  wheel  with  62  teeth  be  fixed  on  a  shaft  making  53.098894 
revolutions  a  minute ;  what  number  of  revolutions  will  a  shaft 
make  with  a  wheel  46  teeth  fixed  on  it,  and  driven  by  the  wheel 
with  62  teeth? 

53.098894  revolutions  of  given  shaft  a  minute. 
62  teeth  in  wheel  on  given  shaft. 


106197788 
318593364 
Teeth  of)  

wheel  on  V  46)3292.131428(71.568074  revolutions  of  shaft  a 
shaft,      j       322  minute. 


72 
46 


261 
230 


313 
276 


371 

368 


342 
322 


208 
184 


24 

If  a  wheel  with  63  teeth  be  fixed  on  a  shaft  making  71.568074 
revolutions  a  minute;  what  number  of  revolutions  will  a  shaft 


SPEED  OF  SHAFTS. 


IT 


make  with  a  wheel  of  45  teeth  fixed  on  it,  and  driven  by  the 
wheel  of  63  teeth? 

71.568074  revolutions  of  shaft  a  min. 
63  teeth  in  wheel. 


214704222 
429408444 


Teeth  of  wheel  on  )  45)4508.788662(100.1953  revolutions  of  shft. 

^      45  a  minute  driving 
  looms. 


087 
45 

428 
405 


238 
225 

136 
135 


If  a  wheel  with  49  teeth  be  fixed  on  a  shaft  making  100.1953 
revolutions  per  minute,  drives  a  wheel  of  38  teeth,  fixed  on  foot 
of  upright-shaft ;  what  revolutions  will  the  upright-shaft  make  a 
minute? 

100.1953  revol.  of  given  shaft  a  minute. 
Teeth  of  wheel  on  shaft  49 


9017577 
4007812 


Teeth  of  wheel  on  J 
foot  of  upright-  V  38)4909.5697(129.2  revolutions  of  upright- 
shaft,  5      38  shaft  a  minute — Spin- 

  ning-room. 

110 
76 


349  76 

342  78— nearly. 


18 


SPEED  OE  SHAFTS. 


If  a  drum  21  inches  diameter  be  fixed  on  an  upright-shaft, 
for  driving  upright-shaft  in  wheelhouse,  making  129.2  revolutions 
a  minute ;  what  number  of  revolutions  a  minute  will  the  upright- 
shaft  in  wheelhouse  make,  with  a  pulley  14  inches  diameter  fixed 
on  it? 

129.2  revol.  a  min.  of  upright-shaft. 
21  inches  diameter  of  drum  on  it. 


1292 
2584 


Inches  diam.  of  pulley,  14)2713.2(193.8 

14 


131 
126 


53 
42 


112 
112 


If  a  wheel  with  60  teeth,  fixed  on  a  shaft,  makes  53.098894 
revolutions  a  minute;  what  number  of  revolutions  per  minute 
will  an  upright-shaft  make,  with  a  wheel  of  44  teeth  fixed  on  its 
foot,  and  driven  by  the  wheel  of  60  teeth? 

53.098894  revolutions  a  minute. 
60  teeth  wheel. 
Teeth  of  wheel  on  ^  

foot  of  upright-  [  44)3185.933640(72.40758  revol.  of  upright- 
shaft,  )      308  shaft  a  min.,  for 

  Dressing-room. 

105 
88 

  256 

179  220 

176   

  364 

333  352 

308   


revolutions  of  upright- 
shaft  in  wheelhouse  a 
minute,  working  rim  or 
fly-shafts. 


SPEED  OF  SHAFTS. 


19 


Or  thus,  dividing  bv  4  and  11  for  44. 

4  <{  3185.93364 

11  79648341 


72.40758—12 


If  an  upright-shaft  makes  72.40758  revolutions  a  minute,  with 
a  wheel  of  75  teeth  fixed  on  top,  working  into  a  wheel  of  41  teeth, 
fixed  on  a  lying-shaft;  what  revolutions  a  minute  will  the  lying- 
shaft  make  ? 

72.40758  revols.  of  upright-shaft  a  min. 
75  teeth  of  wheel. 


36203790 
50685306 


Teeth  of  wheel  on 


Tin  shaft         I  41)54.3056850(132.4529  revolutions  a  min.  of 
°'       '         ^41  shaft  driving  Dress- 


133 
123 

100 

82 


ing-frame. 


185 
164 

216 
205 

118 

82 


365 
369 — nearly. 


The  speed  of  any  shaft  may  he  obtained,  tvithout  ascertaining  the 
speeds  of  the  intermediate  shafts,  by  the  following 

RULE. 

Multiply  the  number  of  double  strokes  of  the  steam-engine,  or 
the  number  of  revolutions  of  any  given  shaft  per  minute  by  the 


20  SPEED  OF  SHAFTS. 


number  of  teeth  in  the  driving-wheels  respectively,  or,  if  drums 
or  pulleys,  by  the  inches  in  the  diameters  respectively,  or  in  the 
place  they  occur,  for  a  dividend,  and  all  the  driven-wheels,  drums, 
or  pulleys,  in  the  same  manner,  for  a  divisor,  and  the  quotient 
will  be  the  speed  of  the  shaft  required. 

If  a  steam-engine  be  making  22  double  strokes  or  revolutions 
a  minute,  with  the  following  driving  and  driven-wheels,  drums, 
and  pulleys ;  what  number  of  revolutions  a  minute  will  the  shaft 
make  which  is  intended  to  drive  a  blowing  machine  or  scutcher  ? 

DRIVING. 

Revolutions  a  minute,  crank 
or  fly-shaft  22. 

Wheel  on  crank  or  fly-shaft 
106  teeth. 

Wheel  on  first  lying-shaft,  driv- 
ing upright-shaft  61  teeth. 

Wheel  on  top  of  upright-shaft 
70  teeth. 

Diameter  of  drum  on  shaft  45  J  [  inches, 
inches.  | 

22  revolutions  a  minute  crank  or  fly-shaft. 
106  teeth  in  wheel  on  crank-shaft. 


132 
220 


2332 

61  teeth  in  wheel  on  first  lying-shaft,  driving 

  upright-shaft. 

2332 
13992 


142252 

70  teeth  in  wheel  on  top  of  upright-shaft. 


9957640 

45.5  or  45J  inches  diameter  of  drum  on  shaft. 


49788200 
49788200 
39830560 


453072620.0  dividend. 


DRIVEN. 

Wheel  on  first  lying-shaft  47 
teeth. 

Wheel  top  of  upright-shaft  57 
teeth. 

Wheel  on  next  lying-shaft,  39 
teeth. 

Diameter  of  pulley  on  shaft  for 
driving  blowinsr  machine  131 


3C 


SPEED  OP  SHAFTS. 


V,-  21' 

47  teeth  in  -wheel  on  first  line  of  shafts.  ''"^  vi^  i\ 
57  teeth  in  wheel  on  foot  of  upright-shaft. 


329 
235 

2679 


39  teeth  in  wheel  on  second  lying-shaft. 


24111 
8037 


104481 

13.75  or  13f  inches  diameter  of  pulley  on  shaft 

 for  driving  blowing  machines. 

522405 
731367 
313443 
104481 


1436613.75  divisor. 

1436613.75)453072620.0(315.375388  revolutions  a  minute,  shaft 
430984125  driving  blowing  machine. 


220884950 
143661375 

772235750 
718306875 

539288750 
430984125 

1083046250 
1005629625 

774166250 
718306875 


558593750 
430984125 


1276096250 
1149291000 

1268052500 
1149291000 


1276096250 


118761500 


22 


SPEED  OF  SHAFTS. 


iV.  B. — The  small  difference  arising  in  the  above  system  of  work- 
ing, is  on  account  of  ivorking  all  the  different  speeds  of  shafts 
separately.    (See  former  Examples.) 

If  a  drum  45J  inches  diameter  be  fixed  on  a  shaft  making 
315.375388  revolutions  a  minute  ;  what  number  of  revolutions 
■will  the  beater  of  a  blowing  machine  make,  with  a  pulley  fixed 
on  the  beater  end,  10  inches  diameter,  and  driven  by  a  strap 
from  the  drum  45 J  inches  diameter? 

315.375388  revolutions  of  shaft  a  minute. 
45.5  or  45J  inches  diam.  of  drum. 


1576876940 
1576876940 
1261501552 

Inches  diam. 


of  pulley  on  1 10)14349.5801540 

beater  end,  j  

1434.9580154  revolutions  of  beater  a  min. 

If  a  shaft  makes  84  revolutions  a  minute,  with  a  wheel  of  60 
teeth  fixed  on  it,  working  into  a  wheel  on  a  cross  or  upright-shaft, 
with  52  teeth ;  what  number  of  revolutions  will  the  cross  or  up- 
right-shaft make? 

84   revolutions  of  shaft  a  minute. 
60  teeth  in  wheel  on  shaft. 


Teeth  of  wheel  on  cross  1  rn\c:n4r\ff\G  noo  1  e 

)- 52)5040(96.923  revols.  of  cross  or  up- 
or  upright-shait,  |       ma  •  i  i.  u  ^i.       •  i. 

^  °  '  468  right-shait  a  minute. 


360 
312 


480 
468 


120 
104 


160 
156 


4 


SPEED  OF  SHAFTS. 


23 


If  a  cross  or  upright-shaft  be  making  96.923  revolutions  a 
minute,  with  a  wheel  of  52  teeth  fixed  on  it,  which  is  driven  by 
a  wheel  with  60  teeth  fixed  on  the  lying-shaft;  what  number  of 
revolutions  will  the  lying-shaft  make  a  minute  ? 

96.923  revols.  a  min.  of  cross  or  upright-shaft. 
52  teeth  of  wheel  fixed  on  shaft. 


193846 
484615 
Teeth  of"|  

wheel  on  V  60)5039.996(84  nearly,  revolutions  of  lying-shaft, 
lying  shft.  j  480 

239 

240 — nearly. 


If  a  drum  18  inches  diameter  be  fixed  on  a  shaft  making 
96.923  revolutions  a  minute;  what  number  of  revolutions  will 
the  main  cylinder  of  a  carding-engine  make,  with  a  pulley  fixed 
on  the  cylinder  end  15  inches  diameter,  and  driven  by  a  strap 
from  the  drum  18  inches  diameter? 

96.923  revols.  a  min.  of  shaft. 
18  inches  diam.  of  drum. 


775384 
96923 


Inches  diameter  of  V^^^^j\i5)iU4.QU{116.Srevoh.  of  main 
on  cylinder  end,  j      ic  i-  j 

'  -'15  cylinder  a  mm. 

24 
15 


94 
90 

46 
45 


Required  the  diameter  of  a  pulley  to  make  116.3  revolutions 


24 


SPEED  OF  SHAFTS. 


a  minute ;  the  drum  fixed  on  the  shaft  being  18  inches  diameter, 
making  96.923  revolutions  a  minute: — 

96,923  revolutions  of  shaft  a  minute. 
18  inches  diameter  of  drum. 


775384 
96923 


Revols.  required  116.3)1744.614(15  in.  diam.  of  pulley  required. 
1163 


5816 
5815 


1 

N.  B. —  The  speed  of  any  piece  of  machinery  may  he  ascertained, 
according  to  the  foregoing  Rules  and  Examples. 

The  speed  of  a  counter-shaft  is  required,  the  following  parti- 
culars being  given : — 

First  shaft  96  revolutions  a  minute. — Drum  on  said  shaft  18 
inches  diameter. — Drum  on  second  shaft  14  inches  diameter. 
— Drum  on  the  second  shaft  for  driving  the  third  shaft  10 
inches  diameter. — Drum  on  the  third  shaft  9  inches  diameter. 

Drum  on  2d  shaft  14  inches  diameter. 
Drum  on  3d  shaft  9  inches  diameter. 


126  divisor. 


96  revolutions  of  shaft  a  minute. 

18  inches  diameter  of  drum  on  this  shaft. 


768 
96 


1728 

10  inches  diameter  of  drum  on  2d  shaft. 


17280 


SPEED  OF  SHAFTS — MIXING  COTTON.  25 

126)17280(137.14  revels,  of  counter-shaft  a  min. 
126 


468 
378 


900 
882 


180 
126 


540 

504 


36 


MIXING  COTTON. 

On  account  of  the  many  varieties  and  variations  even  of  the 
same  kinds  of  cotton,  it  "will  be  found  best  to  mix  a  number  of 
bales  or  bags  together ;  arranging  them  properly  in  the  place 
appropriated  for  the  purpose,  which  done,  proceed  to  throvr 
abroad  one  bale  or  bag,  covering  as  much  surface  as  convenience 
■will  allow,  according  to  the  number  intended  to  be  mixed,  and 
proceed  till  the  last  is  thrown  on  your  stock,  treading  it  well 
down  as  you  proceed.  When  wanted  for  use,  rake  it  down  with 
a  rake,  similar  to  a  garden  rake,  regularly  from  the  top  to  the 
bottom  ;  this  process  will  be  found  not  only  to  mix  it  regularly, 
but  will  open  the  cotton  considerably,  which  is  very  essential, 
prior  to  being  put  through  the  first  preparatory  piece  of  ma- 
chinery. 

In  all  cases  it  is  best  to  mix  as  great  a  number  of  bales  or 
bags  of  cotton  as  can  be  done  conveniently ;  because,  whenever 
there  is  a  fresh  mixing  of  cotton,  it  is  almost  sure  to  require  an 
alteration  in  some  of  the  machinery,  as  it  seldom  happens  that 
the  new  mixing  will  produce  the  same  weight  of  roving  or  yarn. 
3 


26 


MACHINERY — WILLOW. 


MACHINERY. 

In  treating  on  machinery,  the  rules  and  examples  will  be  laid 
down  in  the  most  easy,  plain,  and  simple  manner,  so  that  per- 
sons possessing  only  a  knowledge  of  the  fundamental  rules  of 
arithmetic,  will  be  able  to  comprehend  them :  and  by  following 
the  rules,  examples,  and  illustrations  laid  down,  they  will  be  able 
to  acquire  every  qualification  requisite,  so  far  as  regards  calcula- 
tions, for  persons  filling  the  important  situations  of  managers  or 
overlookers  in  any  or  every  department  of  cotton  manufacturing. 

In  the  succeeding  calculations,  all  common  fractions,  as  far  as 
possible,  are  omitted,  and  decimal  fractions  used.  A  knowledge 
of  decimals  may  be  easily  obtained  from  almost  any  work  on 
Arithmetic;  but  the  best  for  the  mechanic  is  the  Practical  Model 
Calculator,  by  the  editor  of  this  work,  Oliver  Byrne. 

WILLOW. 

Willows  are  generally  used  for  opening  the  cotton,  and  taking 
out  the  heavy  dirt.  They  are  of  various  constructions.  The  one 
of  which  the  following  are  the  particulars,  is  of  recent  construc- 
tion : — 

A  square  cylinder  measuring  30  inches  from  angle  to  angle. 

4  strips,  one  at  each  corner,  4  inches  by  3J  inches. 

4  strips  on  the  top  corners,  4  inches  by  3J  inches. 

8  teeth  or  pins  in  each  strip  on  the  cylinder,  at  a  regular  dis- 
tance from  each  other. 

7  teeth  in  each  strip  on  the  top,  or  cover,  and  set  opposite  the 
centre  of  the  spaces. 

Distance  of  teeth  4  inches;  length  of  teeth  4  inches. 

Diameter  of  teeth  at  bottom  1  inch,  regularly  tapering  to  |  inch. 

Circular  iron  grate  bars,  or  rods,  half  inch  distant  from  each 
other. 

The  time  for  the  cotton  remaining  in  the  willow  is  governed 
by  wheel-work ;  one  of  the  wheels  has  a  pin  fixed  in  it,  and 
every  time  it  revolves,  works  upon  a  spring  connected  with  a 
lever,  which  opens  the  lid  and  discharges  the  cotton. 

N.  B. — It  is  customary  with  some  to  take  off  the  wheels,  having 
the  lid  continually  down,  consequently,  the  cotton  thrown  in 
will  only  revolve  once  or  twice,  before  being  discharged. 


■  t 


BLOWING  MACHINE. 


2T 


This  system  is  adopted  by  the  probability  of  the  cotton  being 
strung,  by  being  too  long  detained  in  the  machine. 

If  the  shaft  for  driving  a  willow  makes  158.84  revolutions  a 
minute,  with  a  drum  fixed  on  it  26  inches  diameter,  and  the 
pulley  on  the  end  of  willow  cylinder  be  12  inches  diameter  ;  what 
number  of  revolutions  will  the  cylinder  make  a  minute  ? 

158.84  revolutions  of  shaft  a  min. 

26  inches  diam.  of  drum  on  shaft. 


95304 
31768 

Inches  diameter  of  ^  

pulley  on  willow- V  12)4129.84 
cylinder  end,  j 


344.15333  revols.  a  min.  of  cylinder. 


BLOWING  MACHINE  WITH  TWO  BEATERS. 

Shaft  for  driving  blowing  machine  315.374  revolutions  a  min. 
Drum  on  said  shaft  45.5  inches  diameter.  Pulley  on  beater  ends 
10  inches  diameter. 

315.374  revolutions  of  shaft  a  min. 
45.5  inches  diam.  of  drum  on  shaft. 


1576870 
1576870 
1261496 


Inches  diameter  of  j  10^14349  5^^0 
pulley  on  beaters,  )  '  


1434.9517  revols.  of  beater  at  blowing 
machine  a  minute. 


If  a  pulley  inches  diameter  be  fixed  on  the  end  of  a 
beater,  making  1535  revolutions  a  minute ;  what  number  of 
revolutions  a  minute  will  a  shaft  make,  with  a  pulley  fixed  on  it 
31  inches  diameter,  and  driven  by  a  strap  from  the  pulley  4.75 
inches  diameter  ? 


28 


BLOWING  MACHINE. 


1435  revolutions  of  beater  a  minute. 
4.75  in.  diam.  of  pul.  on  beater  end. 


7175 
10045 
5740 

Inches  diameter  of)   

pulley  on  under-  V  31)6816.25(219.879  revols.  of  shaft  a  min, 
shaft,  j  62 


61 
31 


306 
279 


272 
248 


245 
217 


280 
279 


1  • 

If  a  -wheel  with  14  teeth  be  fixed  on  the  end  of  the  shaft  at 
blowing  machine,  making  219.879  revolutions  a  minute ;  what 
number  of  revolutions  a  minute  will  a  shaft  make  with  a  wheel  of 
88  teeth,  fixed  on  the  end,  and  driven  by  a  wheel  of  14  teeth  ? 

219.879  revolutions  of  given  shaft  a  min. 
14  teeth  wheel  on  end  of  shaft. 


879516 
219879 


8078,306 


BLOWING  MACHINE.  29 


Teeth  of  wheel  on 


F  wheel  on  Igg.gQ^g  gQQ.gj  gg  ^^^^^^^  geering-shaft 
ffeerms-shait,        I      op  i  •  i 

^       "        '  264  a  minute. 


438 
352 

 k 

863 
792 


710 
704 


6 


If  a  wheel  with  35  teeth  be  fixed  on  the  other  end  of  geering- 
shaft,  working  into  wheel  35  teeth  on  bottom  of  bevil-shaft,  and 
a  wheel  35  teeth  on  the  top.  of  bevil-shaft,  be  working  into  a 
wheel  60  teeth  on  the  end  of  creeper,  or  delivering-roller ;  what 
revolutions  will  the  creeper,  or  delivering-roller  make  a  minute  ? 

34.98  revols.  of  geering-shaft  a  min. 
35  teeth  wheel  on  top  of  bevil-shaft. 

17490 
10494 

Teeth  of  wheel  on^  

end    of    creeper- V  60)1224.30 

roller,  j  

20.405  revols.  of  creeper,  or  delivering- 
roller,  a  minute. 

I^.JB. —  The  35  teeth  wheels  on  end  of  geering-shaft,  and  bottom 
of  bevil-shaft  are  omitted,  on  account  of  their  being  the  same 
as  carrying,  or  connecting  wheels  only. 

If  a  wheel  of  18  teeth  be  fixed  on  creeper,  or  delivering-roller, 
making  20.405  revolutions  a  minute,  working  into  a  wheel  on 
stud  with  40  teeth,  which  works  into  a  wheel  of  64  teeth  on 
another  stud,  which  works  into  wheel  of  96  teeth  on  the  front, 
or  second  wire  cylinder  end;  what  number  of  revolutions  will 
the  cylinder  make  a  minute? 


30 


BLOWING  MACHINK. 


JSf.  B. — All  the  intermediate  wheels  between  the  creeper-roller  and 
wheel  on  wire  cylinder  end  are  omitted  in  the  operation^  being 
only  carrying,  or  connecting  wheels,  which,  if  made  use  of, 
must  be  considered  as  both  driving  and  driven-wheels. 


20.405  revols.  of  creeper-roller  a  min. 
18  teeth,  wheel  on  end  of  roller. 


163240 
20405 


Teeth  of  wheel  on  |  96)367,290(3.826  nearly  revols.  2d  wire 
wire  cylinder  end,   /     ^388      ^         cylinder  a  minute. 


792 
768 


249 
192 


570 

576 — nearly. 

If  a  wheel  with  52  teeth  be  fixed  on  the  end  of  geering-shaft, 
making  34.98  revolutions  a  minute,  working  into  a  wheel  of  52 
teeth  (a  shaft  which  is  the  length  of  the  machine,  for  propelling 
the  shafts  of  the  feed-rollers);  on  the  lying-shaft  is  a  wheel  with 
50  teeth  working  into  a  wheel  on  the  bottom  of  upright-shaft 
40  teeth,  and  a  wheel  with  39  teeth  on  the  top  of  upright-shaft, 
working  into  a  wheel  82  teeth  on  the  end  of  the  feed-rollers; 
what  number  of  revolutions  will  the  feed-rollers  make  ? 


iV.  B. —  The  first  two  wheels,  52  teeth  each,  are  omitted,  being  only 
carrying  or  connecting  wheels. 

When  there  are  more  than  one  driving  and  driven-wheels, 
multiply  the  revolutions  a  minute  of  your  given  shaft  by  the  driv- 
ing-wheels respectively  for  a  dividend,  and  your  driven-wheels 
(only)  together  for  a  divisor,  and  the  quotient  will  be  the  revolu- 
tions a  minute  required. 


BLOWINa  MACHINE. 


31 


34.98   revolutions  of  given  shaft  a  minute. 
50  teeth  wheel  first  driver. 


1749.00 


39  teeth  wheel  top  of  upright-shaft  working 
  into  wheel  82  teeth  on  roller  end. 


15741 
5247 


68211  dividend. 


40  teeth  wheel  on  bottom  of  upright-shaft. 
82  teeth  wheel  on  feed-roller  end. 


3280  divisor. 

3280)68211(20.796  revols.  a  min.  of  2d  feed-roller. 
6560 


26110 

22960 


31500 
29520 


19800 
19680 


120 

If  a  wheel  with  12  teeth  be  fixed  on  the  end  of  the  feed-rollers, 
making  20.793  revolutions  a  minute,  works  into  a  stud-wheel  26 
teeth,  which  works  into  wheel  26  teeth  on  the  first  creeper-roller 
end;  what  number  of  revolutions  a  minute  will  the  first  creeper- 
roller  make? 


20.793  revols.  of  2d  feed-roller  a  min. 
12  teeth  in  wheel  on  feed-roller. 


Teeth  of  wheel  on 
1st  creeper, 


26)249.516(9.6  revols.  of  1st  creeper-roller 
234  a  minute. 


155 

156 — nearly. 


32 


BLOWING  MACHINE. 


If  a  wheel  with  16  teeth  be  fixed  cn  the  first  creeper-roller, 
making  9.0  revolutions  a  minute,  works  into  a  stud-wheel  96 
teeth  (carrier),  which  works  into  wheel  of  96  teeth  on  first  wire 
cylinder  end ;  what  number  of  revolutions  will  the  first  wire  cylin- 
der make  a  minute? 

9.6  revols.  of  first  creeper-roller  a  min. 
16  teeth-wheel  fixed  on  first  creeper-roller. 

676 
96 

Teeth  of  wheel  1  9(3\i53  gn  g  revols.  of  1st  wire  cyl.  a  minute, 
on  1st  wire  cyl.  J  qq 


576 
576 


If  a  wheel  with  40  teeth  be  fixed  on  a  lying-shaft,  making 
34.98  revolutions  a  minute,  works  into  a  wheel  50  teeth  on  the 
bottom  of  an  upright-shaft,  and  a  wheel  40  teeth  fixed  on  the 
top  of  upright-shaft  works  into  wheel  82  teeth  on  end  of  feed- 
rollers;  what  number  of  revolutions  will  the  first  feed-roller  make 
a  minute  ? 

Wheel  on  bottom  of  upright-shaft  50  teeth. 
Wheel  on  1st  feed-roller  end         82  teeth. 


4100  divisor. 


34.98  revolutions  of  lying-shaft  a  minute. 
40  teeth  wheel  on  lying-shaft. 

1399.20 

40  teeth  wheel  on  top  of  upright-shaft. 

4100)55968.00(13.65  revolutions  of  1st  feed-roller  a  min. 
41 


149 
123 


266 
246 


208 
205 


BLOWING  MACHINE. 


33 


If  a  wheel  with  12  teeth  fixed  on  the  end  of  feed-rollers,  making 
13.65  revolutions  a  minute,  works  into  a  wheel  of  26  teeth  on 
feed-cloth-roller ;  what  number  of  revolutions  a  minute  will  the 
feed-cloth-roller  make? 

13.65  revols.  of  feed-roller  a  min. 
12  teeth  wheel  on  end. 


Teeth  of  wheel  on  end  of  1 26)163.80(6.8  revols.  of  feed-cloth- 
feed-cloth-roller,  /  roller  a  minute. 


78 
78 

If  the  feed-cloth-roller  be  3  inches  diameter,  making  6.3  revo- 
lutions a  minute;  how  many  inches  will  the  feed-cloth  traverse? 

6.3  revols.  of  feed-cloth-roller  a  minute. 
3  inches  diameter  of  feed-cloth-roller. 


18.9 

3.1416  circumference  when  the  diam.  is  1. 


1131 
189 
756 
189 
567 


69.37624  inches  feed-cloth  traverses  a  min. 

If  the  first  creeper-roller  be  3.5  inches  diameter,  making  9.6 
revolutions  a  minute;  how  many  inches  will  it  traverse? 

3.1416  circumference  when  the  diameter  is  1. 
3.5  diameter  of  creeper-roller. 


157080 
94248 


10.99560  inches  circumference  of  creeper-roller. 
9.6 


6597360 
9896040 


105.557760  inches  first  creeper-roller  traverses  a  min. 


34 


BLOWING  MACHINE. 


If  the  second  feed-roller  be  1.5  inch  diameter,  making  20.793 
revolutions  a  minute ;  how  many  inches  will  it  traverse  ? 

3.1416  circumference  when  the  diameter  is  1. 
1.5  diameter  of  feed-roller. 


157080 
31416 

4.71240  inches  circumference  of  feed-roller. 
20.793 

141372 
424116 
329868 
942480 


97.9849332,  or  nearly  98  inches  feed-roller  traverses 
a  minute. 

If  the  second  creeper,  or  delivering-roller,  be  3.5  inches  di- 
ameter, making  20.405  revolutions  a  minute;  how  many  inches 
will  it  traverse? 

3.1416  circumference  when  the  diameter  is  1. 

3.5  inches  diameter  of  second  creeper,  or  de- 

  livering-roller. 

157080 
94248 


10.99560  inches  circumference  of  second  creeper,  or 
20.405  delivering-rollers. 


649780 
4398240 
2199120 


224.3652180  inches  creeper,  or  delivering-roller,  traverses 

a  minute. 

N.B. —  The  draught  of  any  jriece  of  machinery  may  be  ascer- 
tained by  dividing  the  distances  traversed,  into  each  other,  as 
will  appear  in  a  future  part  of  this  tvorlc. 


DIMENSIONS  AND  MOTIONS  OF  A  DOUBLE  BLOWING  MACHINE.  35 


DIMENSIONS  AND  MOTIONS  OF  A  DOUBLE  BLOWING  MACHINE. 

Beaters  make  1435  revolutions  a  minute. 

Feed-cloth-roller  makes  6.3  revolutions  a  minute. 

First  feed-roller  makes  13.65  revolutions  a  minute. 

First  creeper-roller  makes  9.6  revolutions  a  minute. 

First  wire  cylinder  makes  1.6  revolutions  a  minute. 

Second  feed-roller  makes  20.8  revolutions  a  minute. 

Second  creeper,  or  delivering-roller,  in  the  front  of  machine, 

makes  20.405  revolutions  a  minute. 
Second  wire  cylinder  makes  4.888  revolutions  a  minute. 
Distance  of  grate-bars  from  each  other  J  an  inch. 
Distance  of  grate-bars  from  beaters  1|-  to  J  an  inch. 
Diameter  of  beaters  18  inches. 
Diameter  of  feed-cloth-rollers  3  inches. 
Diameter  of  iron-feed-rollers  IJ  inch. 
Diameter  of  plain  iron-rollers  2  inches. 
Diameter  of  creeper-rollers  3|  inches. 
Diameter  of  wire  cylinder  22  inches. 

]^.B. — The  rollers  not  named  a  second  time  are  of  the  same  di- 
mensions as  those  above. 

Feed-cloth-roller  traverses  59.37624  inches  a  minute. 
First  creeper-roller  traverses  105.55776  inches  a  minute. 
Second  feed-roller  traverses  98  inches  a  minute — nearly. 
Second  creeper,  or  delivering-roller,  traverses  224.365218  inches 
a  minute. 

N.B. —  The  above  particulars  ivill  materially  differ  from  some 
blowing  machines,  but  the  particulars  of  any  machine  may  be 
found  by  following  the  examples  and  illustrations  laid  down. 

LAP  MACHINE. 

It  has  become  very  general  of  late  years  to  have  two  lap  ma- 
chines, in  place  of  a  blowing  machine  and  a  lap  machine,  and 
where  it  is  the  case,  two  or  three  laps  from  the  first  machine  are 
put  up  at  the  second,  which  has  a  great  tendency  to  equalize  the 
lap,  and  produce  more  even  carding;  however,  the  following  are 
the  particulars  where  only  a  certain  weight  is  fed  on  a  given 
length  of  the  feed-cloth  without  any  doubling,  but  there  will  be 
little  difference  in  the  machine  further  than  the  diiference  at  the 
feeding  parts,  or  in  the  draughts  of  the  machine. 


36 


LAP  MACHINE. 


If  the  shaft  for  driving  a  lap  machine  makes  315.3747  revo- 
lutions a  minute,  the  drum  on  said  shaft  40.5  inches  diameter, 
and  the  pulley  on  the  beater  end  11.25  inches  diameter;  how 
many  revolutions  will  the  beater  make  a  minute? 

315.3747  revolutions  of  shaft  a  minute. 
40.5 


15768735 
126149880 


Inches  diam.  \  ii.25)12772.67535(1135.3489  revols.  of  beater 
of  pulley,      /  ^ 


a 

1125  minute. 

1522 
1125 


3976 
3375 


6017 
5625 

3925 
3375 

5503 
4500 

10035 
9000 

10350 
10125 

225 

If  a  pulley  4.75  inches  diameter  be  fixed  on  the  end  of  a  beater 
making  1135.3489  revolutions  a  minute ;  what  revolutions  a 
minute  will  a  shaft  make  with  a  pulley  fixed  on  it  31.5  inches 
diameter,  and  driven  by  a  strap  from  the  pulley  4.75  inches 
diameter  ? 


LAP  MACHINE. 


37 


1185.3489  revolutions  of  beater  a  min. 
4.75  in.  diam.  of  pulley  on  beater 

=   end. 

56767445 
79474423 
45413956 


Inches  diam  of  J  31,5)5392.907275(171.2  revols.  of  shaft  work- 
pulley  on  shaft,  ^  r  ^  •  •  •  , 
^     *'           ^  ^        315                     mg  geering  a  minute. 


2242 
2205 


379 
315 


640 

630 


10 


If  a  wheel  14  teeth  be  fixed  on  shaft  making  171.2  revolu^ 
tlons  a  minute,  and  works  into  a  carrying-wheel  with  30  teeth, 
which  drives  a  wheel  88  teeth  on  geering-shaft ;  what  number  of 
revolutions  a  minute  will  the  geering-shaft  make. 

171.2  revols.  of  shaft  a  min.  working  geering, 
14  teeth  wheel  fixed  on  said  shaft. 


6848 
1712 

Teeth  of  wheel  )   ' 

on  geering-  >  88)2396.8(27.236  revols.  a  minute  of  geering- 
shaft,  )      176  shaft. 


636 
616 


208 
176 

320 
264 


560 
628 


38 


LAP  MACHINE. 


If  a  wheel  with  16  teeth  be  fixed  on  a  shaft  making  27.236 
revolutions  a  minute,  works  into  a  wheel  88  teeth  on  the  end  of 
lap-roller;  how  many  revolutions  will  the  lap-roller  make  a 
minute  ? 

27.236  revolutions  of  shaft  a  minute. 
16  teeth  wheel  on  said  shaft. 


163416 
27236 

kprol^er^^^^^     \  ^^vols.  of  lap-roller  a  min. 


837 
792 


457 
440 


176 
176 

iV.  B. — There  is  a  wheel  of  30  teeth  fixed  on  the  first  lap-roller^ 
which  tvorJcs  into  a  wheel  20  teeth  on  stud,  which  drives  a 
wheel  30  teeth  on  the  second  lap-roller,  consequently  it  will  he 
the  same  speed  as  the  first. 

If  a  wheel  22  teeth  fixed  on  geering-shaft,  make  27.236  revo- 
lutions a  minute,  works  into  a  wheel  88  teeth  on  front  iron-roller; 
what  number  of  revolutions  will  the  front  iron-roller  make  a 
minute  ? 

27.236  revols.  of  geering-shaft  a  min. 
22  teeth  wheel  on  geering-shaft. 


54472 
54472 

Teeth  of  wheel  on  )  88)599.192(6.809  revolutions  of  front  iron- 
iront  iron-roller,  \     Voo  n         •  i. 

'         ozo  roller  a  minute. 


711 
704 


792 
792 


ii 


LAP  MACHINE. 


39 


If  a  'wheel  of  20  teeth  fixed  on  the  front  iron-roller,  making 
6.809  revolutions  a  minute,  works  into  a  wheel  of  19  teeth  on 
stud,  which  works  into  a  wheel  of  19  teeth  on  creeper-roller; 
what  number  of  revolutions  will  the  creeper-roller  make  a  minute  ? 

6.809  revolutions  of  iron-rollers  a  min. 
20  teeth  wheel  fixed  on  iron-rollers, 

Teethof  wheel  on  |  i9^i36.i80(7.167  revol.  of  creeper-roller  a 
creeper-roller,     /  ^^33 


31 
19 

128 
114 

140 
183 


If  a  wheel  of  18  teeth  fixed  on  the  end  of  creeper-roller,  making 
7.167  revolutions  a  minute,  works  into  a  wheel  with  64  teeth  on 
stud,  which  works  into  a  wheel  of  96  teeth  on  wire  cylinder  end; 
what  number  of  revolutions  will  the  wire  cylinder  make  a  minute  ? 

7.167  revols.  of  creeper-roller  a  min. 
18  teeth  wheel  fixed  on  creeper-roller. 


57336 
7167 


Teeth  of  wheel  on 


a^eemoiwneeion  96)129.006(1.3438  revols.  of  wire  cyl.  a  min. 
Wire  cylinder,      )  qp 


96 

830 
288 

420 
384 


— -  780 

366  768 
288  


40 


LAP  MACHINE. 


If  a  wheel  with  36  teeth,  fixed  on  the  end  of  the  creeper-roller, 
making  7.167  revolutions  a  minute,  works  into  a  wheel  with  36 
teeth  on  feed-roller  shaft,  and  on  the  other  end  of  feed-roller 
shaft  is  a  wheel  with  46  teeth,  which  works  into  a  wheel  with  30 
teeth  on  feed-roller  end ;  what  number  of  revolutions  will  the 
feed-rollers  make  a  minute? 

7.167  revols.  of  creeper-roller  a  min. 
46  teeth  on  end  of  feed-roller  shaft. 

43002 
28668 

Teeth  of  wheel  on 
feed-roller, 

10.9894  nearly  11  revolutions  of  feed- 
rollers  a  minute. 

N'.  B. — The  two  36  teeth  wheels  are  not  noticed,  the  one  being  a 
driver,  and  the  other  driven. 

If  a  wheel  with  12  teeth  fixed  on  feed-rollers,  making  10.9894 
revolutions  a  minute,  works  into  a  stud-wheel  of  26  teeth,  work- 
ing into  wheel  of  26  teeth  on  feed-cloth-roller  end;  what  number 
of  revolutions  will  the  feed-cloth-roller  make  a  minute? 


30)329.682 


10.9894  revols.  of  feed-roller  a  min. 
12  teeth  wheel  on  feed-rollers. 


Teeth  of  wheel  on  1  26)181.8728(5.072  revols.  of  feed-cloth- 
feed-cloth-roller,      /       ^^3^  roller  a  minute. 


187 

182 


52 
52 


What  number  of  inches  will  the  feed-cloth  traverse  a  minute, 
if  the  diameter  of  feed-cloth-roller  be  3  inches,  making  5.072 
revolutions  a  minute  ? 


LAP  MACHINE. 


41 


N.  B. —  To  find  the  circumference  of  wheels,  drums,  pulleys,  roll- 
ers, ffc,  multiply  the  diameters  hy  3.1416,  tuhich  is  equal  to  the 
circumference  when  the  diameter  is  1. 

5.072  revols.  of  feed-cloth  roller  a  min. 
3  inches  diameter  of  feed-cloth-rol. 


15.216 
3.1416 


91296 
15216 
60864 
15216 
45648 


47.8025856  being  rather  more  than  47|  in. 

feed-eloth  traverses  a  minute. 

If  the  feed-rollers  of  lap  machine  be  1|  inch  diameter,  making 
10.9894  revolutions  a  minute;  what  number  of  inches  will  they 
traverse  a  minute? 

10.9894  revolutions  of  feed-rollers  a  min. 
1.5  inch  diameter  of  feed-rollers. 


549470 
109894 


16.48410 

3.1416  cii'cumference  when  the  diam.  is  1. 


989046 
164841 
659364 
164841 
494523 


51.78644856  inches  feed-rols.  traverse  a  min. 

What  is  the  draught  between  feed-cloth  and  feed-rollers,  from 
the  two  preceding  examples? 
4 


42 


LAP  MACHINE. 


Inches  feed-cloth  traverses.    Inches  feed- rollers  traverse. 

47.8025856)51.78644856(1.083  inch  draught  be- 
478025856  tween  feed-cloth 

 and  feed-roller. 

3983862960 
3824206848 


1596561120 
1434077568 


162483552 

If  the  creeper-roller  at  lap  machine  be  3|  inches  diameter, 
making  7.167  revolutions  a  minute;  what  number  of  inches  will 
it  traverse  in  a  minute  ? 

7.167  revolutions  of  creeper-roller  a  minute. 
3.5  inches  diameter  of  creeper-roller. 

35835 
21501 


25.0845 

3.1416  equal  to  circumference  when  diam.  is  1. 


1505070 
250845 

1003380 

250845 
752535 


78.80546520  inches  creeper  traverses  a  minute. 

Required  the  draught  between  the  feed-rollers  and  the  creeper ; 
the  feed-rollers  traversing  51.78644856  inches  a  minute,  and  the 
creeper  the  same  as  in  the  preceding  example. 


LAP  MACHINE. 


43 


Inches  feed-rollers  traverse.    Inches  the  creeper  traverses. 

51.78644856)78.80546520(1.5217  draught  between 
5178644856  feed-roller  and 

creeper-rollers. 


27019016640 
25893224280 

11257923600 
10357289712 

9006338880 
5178644856 

38276940240 
36250513992 

2026426248 


If  the  iron-roller  in  front  of  lap  machine  be  3  j  |  inches  diame- 
ter, making  6.809  revolutions  a  minute;  what  number  of  inches 
will  it  traverse  a  minute? 

f4)15.00  decimal  of}!  =  .9375 
16^ 


(  4)3.75 

  inches.       6.809  revols.  of  iron-rol.  a  min. 

.9375  therefore=3i|  =  3. 9375  inches  diam.  on  iron-rol. 


34045 
47663 
20427 
61281 
20427 

26.8104375 

3.1416  circum.  when  diam.  is  1. 


1608626250 
268104375 
1072417500 
268104375 
804313125 


84.22767045000  inches,  or  84}  inches 
nearly,  iron-roller  front  of  lap  machine  traverses  a  minute. 


44 


LAP  MACHINE. 


Required  the  draught  between  creeper-roller  and  iron-roller, 
from  the  preceding  examples. 
Inches.  Inches. 

78.8)84.22767(1.068  draught  between  creeper-roller 
788  and  iron-roller  at  lap  machine. 


5427 
4728 

  6927 


6996  6304 
6304   


623 


B. — It  is  not  practically  necessary  or  requisite  to  carry  any 
examples  to  more  than  3  or  4  decimal  figures,  however  they  may 
occur  in  multiplying ;  hut  they  may  be  used  if  thought  proper 
in  dividing. 

If  the  lap-roller  be  6|  inches  diameter,  making  4.952  revolu- 
tions a  minute;  how  many  inches  will  it  traverse  a  minute? 

4.952  revolutions  of  lap-roller  a  minute. 
6.5  inches  diameter  of  lap-roller. 


24760 
29712 

32.1880 
3.1416 

193128 
32188 
128752 
32188 
96564 

101.1218208  inches  lap-roller  traverses  a  minute. 

Required  the  draught  between  the  iron-roller  and  the  lap-roller, 
from  the  preceding  examples. 

Inches.    Inches  lap-roller  traverses  a  minute. 
84,2276)101.1218208(1.2  draught  between  iron-roller  and 
842276  lap-roller. 

1689422 
1684552 

4870 


LAP  MACHINE. 


The  total  draught  at  the  lap  machine  may  be  ascertained  by. 
multiplying  the  diflferent  draughts  into  each  other : 

OR, 

By  multiplying  all  the  driving-wheels  together,  beginning  at 
the  wheels  driving  the  lap-roller,  and  taking  them  respectively 
(except  the  driving  and  driven-wheels,  which,  being  of  the  same 
number  of  teeth,  are  omitted)  to  the  feed-cloth-roller,  the  pro- 
duct of  which  must  be  multiplied  by  the  diameter  of  the  feed- 
cloth-roller,  for  a  divisor,  and  all  the  driven-wheels  multiplied  in 
the  same  manner,  the  products  of  which  must  be  multiplied  by 
the  diameter  of  the  lap-roller  for  a  dividend,  and  the  quotient 
will  be  the  draught,  as  in  the  following  examples: — 

Draught  between  feed-cloth  and  feed-rollers  1.08. 
Draught  between  feed-roller  and  creeper-roller  1.52. 
Draught  between  creeper-roller  and  iron-roller  1.068. 
Draught  between  iron-roller  and  lap-roller  1.2. 

1.08  draught  between  feed-cloth  and  feed-rollers. 
1.52  draught  between  feed-roller  and  creeper-roller. 

216 
540 
108 


1.6416 

1.0688  draught  between  creeper-roller  and  iron-roller. 


131328 
131328 
98496 
164160 


1.75454208 

1.2  draught  between  iron-roller  and  lap-roller. 

350908416 
175454208 


2.105450496  total  draught  at  lap  machine. 

THE  SAME  EXAMPLE  AS  LAST — BY  WHEELS. 

The  first  driven- wheel  on  lap-roller  is  88  teeth,  working  into  a 
•wbeel  16  teeth  on  the  end  of  geering-shaft ;  then  on  the  other 


46 


LAP  MACHINE. 


end  of  geering-shaft  there  is  a  wheel  with  22  teeth,  working  into 
a  wheel  with  88  teeth  on  iron-roller;  on  the  other  end  of  iron- 
roller  a  wheel  with  20  teeth  works  into  a  wheel  with  20  teeth  on 
the  top-roller,  which  works  into  a  wheel  with  20  teeth  on  a  stud, 
which  works  into  a  wheel  with  19  teeth  on  the  creeper-roller  end; 
on  the  other  end  of  creeper-roller  there  is  a  wheel  with  36  teeth, 
working  into  a  wheel  with  36  teeth  on  the  end  of  the  feed-roller- 
shaft;  on  the  other  end  of  the  feed-roller-shaft  there  is  a  wheel 
with  46  teeth  working  into  a  wheel  with  30  teeth  on  the  end  of 
the  feed-roller;  on  the  other  end  of  the  feed-roller  there  is  a 
wheel  with  12  teeth  working  into  a  wheel  with  26  teeth  on  a  stud, 
which  works  into  a  wheel  with  26  teeth  on  the  end  of  the  feed- 
cloth-roller  ;  the  lap-roller  is  6|  inches  diameter,  and  the  feed- 
cloth-roller  3  inches  diameter;  what  is  the  draught  at  lap 
machine  ? 

DRIVING-WHEELS. 

88  teeth  wheel  on  lap-roller. 
22  teeth  wheel  on  geering-shaft. 

176 
176 


1936 

20  teeth  wheel  on  iron-roller. 


38720 

46  teeth  wheel  on-  feed-shaft. 


232320 
154880 


1781120 

12  teeth  wheel  on  feed-roller. 


21373440 

3  inches  diameter  of  feed-cloth-roller. 


64120320  divisor. 

JV.  B. —  The  carrying^  or  connecting  wheels,  and  driving  and 
driven-wheels  working  together,  where  they  contain  the  same 
number  of  teeth,  are  omitted,  as  will  be  found  in  the  preceding 
and  following  examples: — 


LAP  MACHINE. 


»RIVEN-WHEELS. 

16  teeth  wheel  on  geering-shaft. 
88  teeth  wheel  on  iron-roller. 


128 
128 


1408 

19  teeth  wheel  on  ereeper-roller. 


12672 
1408 


26752 

30  teeth  wheel  on  feed-roller. 


802560 

26  teeth  wheel  on  feed-cloth-roller. 


4815360 
1605120 


20866560 

6.5  diameter  of  lap-roller. 

104382800 
125199360 


135632640.0  dividend. 


Divisor. 

64120320)135632640(2.115  draught  at  lap  machine. 
128240640 


73920000 
64120320 


97996800 
64120320 


338764800 
320601600 


18163200 


48 


CARDING-ENGIISiE. 


iV.  B. —  The  small  difference  hetiveen  the  last  two  examples  is  in 
the  method  of  ivorldng,  arising  from  the  decimal  parts ;  how- 
ever, working  draughts  by  wheels,  as  in  the  last  example,  is  the 
surest  ^vay  where  great  accuracy  {which  is  indispensable),  is 
required. 

The  following  are  the  particulars  of  a  lap  machine,  where 
there  are  no  doublings : — 

Beater  makes  1135.348  revolutions  a  minute. 
Feed-cloth-roller  makes  5.072  revolutions  a  minute. 
Feed-rollers  make  10.9894  revolutions  a  minute. 
Creeper-roller  makes  7.167  revolutions  a  minute. 
Iron-rollers  make  6.809  revolutions  a  minute. 
Lap-rollers  make  4.952  revolutions  a  minute. 

Distance  of  grate-bars  from  each  other  |  an  inch. 
Distance  of  grate  from  beater  1  inch. 
Diameter  of  beater  18  inches. 
Diameter  of  feed-cloth-roller  3  inches. 
Diameter  of  feed-rollers  1|  inch. 
Diameter  of  creeper-roller  3J  inches. 
Diameter  of  iron-rollers  3J|  inches. 
Diameter  of  lap-rollers  6|-  inches. 

Feed-cloth-roller  traverses  47.7025856  inches  a  minute. 
Feed-rollers  traverse  51.78644856  inches  a  minute. 
Creeper-rollers  traverse  78.8054652  inches  a  minute. 
Iron-rollers  traverse  84.2276704  inches  a  minute. 
Lap-rollers  traverse  101.12182808  inches  a  minute. 

Draught  between  feed-cloth  and  feed-rollers  1.108. 
Draught  between  feed-rollers  and  creeper  1.52. 
Draught  between  creeper  and  iron-rollers  1.0688. 
Draught  between  iron-rollers  and  lap-rollers  1.2. 

Total  draught  at  lap  machine  2.115. 

CARDING-ENGINE. 

Carding-engines  are  of  various  constructions,  but  the  construc- 
tion of  machinery  will  make  no  difference  in  the  system  of  cal- 
culation, as  all  the  various  speeds,  &c.,  are  ascertained  from  that 
part  which  first  receives  motion,  which  is  without  exception  the 
main  cylinder. 


4 


CARDING-ENGINE. 


49 


The  opinions  of  persons  connected  with  cotton  carding  are  dif- 
ferent; however,  all  nearly  agree  in  the  most  essential  points, 
that  is,  in  having  the  cards  true  and  sharpened  to  a  diamond 
point,  and  whether  worked  with  rollers,  rollers  and  clearers, 
rollers  clearers  and  part  Jlats,  or  all  flats,  to  have  the  wire  set 
near  as  possible,  so  as  not  to  touch  each  other,  the  first  3  or  4 
flats  set  rather  more  on  the  heel,  or  back  of  card,  for  the  purpose 
of  detaining  the  heavy  dirt.  Some  kinds  of  cotton  require  con- 
siderably more  carding  than  others  ;  however,  it  may  be  observed, 
that  the  less  cotton  is  carded  the  better,  so  that  the  dirt  is  taken 
out,  and  the  fibres  laid  straight,  after  which,  the  cotton  by  being 
continued  in  the  cards  is  only  iveakened,  consequently  the  yarns 
will  be  weakened  in  proportion,  which  must  appear  reasonable  to 
any  practical  person. 

If  a  shaft  make  95.3057  revolutions  a  minute,  with  a  drum 
fixed  on  it  16  inches  diameter;  what  number  of  revolutions  a 
minute  will  the  main  cylinder  of  a  carding-engine  make,  with  a 
pulley  fixed  on  it  14  inches  diameter,  and  driven  with  a  strap 
from  the  drum  16  inches  diameter? 

95.3057  revolutions  of  shaft  a  minute. 
16  inches  diameter  of  drum. 


If  the  main  cylinder  of  a  carding-engine  makes  108.92  revo- 
lutions a  minute,  with  a  wheel  on  its  axis  of  22  teeth,  working 
into  a  wheel  of  140  teeth  on  stud — on  same  stud  there  is  a  wheel 
of  32  teeth,  working  into  a  wheel  of  130  teeth  on  a  stud,  which 
drives  a  wheel  of  130  teeth  on  end  of  dofi"er-cylinder — what  num- 
ber of  revolutions  will  the  main  cylinder  make  for  the  dofi'er- 
cylinder  one,  and  what  number  of  revolutions  will  the  doffer- 
cylinder  make  a  minute  ? 


5718342 
953057 


Inches  diam.  of 
pulley. 


14)1524.8912(109  revols.  of  main  cylinder  a 
14  minute. 


124 


126 — nearly. 


50  CARDING-ENGINE. 

140  teeth  wheel  on  stud. 
130  teeth  wheel  on  doffer-cylinder  end. 


4200 
140 


18200  divisor. 


108.92  revolutions  of  main  cylinder  a  min. 
22  teeth  wheel  on  axis  of  cylinder. 


21784 
21784 


2396.24 

32  teeth  wheel  on  stud. 


479248 
718872 


18200)76679.68(4.213  revols.  of  doffer-cylinder  a  min. 
72800 


38796 
36400 


23968 
18200 


57680 
54600 


3080 

The  revolutions  of  the  main  cylinder  for  the  doflFer- cylinder 
one,  will  be  found  by  dividing  the  revolutions  of  the  main  cylin- 
der by  the  revolutions  of  the  doffer-cylinder. 


CARDING-ENGINE. 


51 


Revols.  of  doffer-cyl.  4.213)108.92(25.85  revols.  of  main  cyl.  for 

8426  doffer  1. 


24660 
21065 


35950 
33704 


22460 
21065 


1395 

The  number  of  revolutions  the  main  cylinder  makes  for  the 
doffer-cylinder  one,  will  be  found  by  multiplying  the  driving- 
wheels  together  for  a  divisor,  and  the  driven-wheels  together  for 
a  dividend,  as  in  the  following  example: — 

DRIVING-WHEELS. 

Wheel  on  cylinder  end  22  teeth. 
Wheel  on  stud  32  teeth. 


44 
66 


704  divisor. 

DRIVEN-WHEELS. 

Wheel  on  stud  140  teeth. 
Wheel  on  doffer-cylinder   130  teeth. 


4200 
140 


18200  dividend. 
704)18200(25.85  revols.  main  cylinder  makes  for 
1408  doffer-cylinder  1. 


4120 
3520 

  3680 

6000  3520 
5632   


52 


CARDING-ENGINE. 


What  will  the  main  cylinder  of  a  carding-engine  traverse  a  min. 
if  it  makes  108.92  revolutions,  and  its  diameter  be  37  inches? 

108.92  revols.  of  main  cyl.  a  minute. 
37  inches  diam.  of  main  cylinder. 

76244 
32676 


4030.04 

3.1416  circum.  when  the  diam.  is  1. 


2418024 
403004 

1612016 

403004 
1209012 


1  foot  =  12  in.)12660.773664 


1  yard  =  3  feet)1055.064472 


inches  main  cyl.  trav.  a  minute, 
feet  main  cyl.  trav.  a  minute. 


351.688157333  yards  main  cyl.  trav.  a  min. 

What  surface  will  the  doffer-cyl.  of  a  carding-engine  traverse 
a  minute,  if  it  makes  4.213  revolutions,  and  is  18  inches  diameter? 

4,213  revolutions  of  doffer-cyl.  a  minute. 
18  inches  diameter  of  doffer-cylinder. 


33704 
4213 


75.834 

3.1416  circumference  when  the  diam.  is  1. 


455004 
75834 

303336 

76834 
227502 


1  foot  =  12  in.)238.2400944  inches  doffer-cyl.  trav.  a  minute. 


1  yard  =  3  feet  )19.8533412  feet  doffer-cyl.  trav.  a  minute. 


6.6177804  yards  doffer-cyl.  trav.  a  minute. 


4 


CARDING-ENGINE. 


53 


How  many  feet  of  fillet,  2  inches  wide,  will  it  require  to  cover 
a  doffer-cylinder  18  inches  diameter,  and  36  inches  wide  ? 

3.1416  circumference  when  the  diam.  is  1. 
18  inches  diameter  of  doffer-cylinder. 


251328 
31416 


56.5488 

36  inches  width  of  doffer-cylinder. 


3392928 
1696464 


orfiHet^^^*^  I  2)2035.7568  inches  area  of  doffer-cylinder. 
1  foot  =  12  in.)1017.8784  inches  of  fillet  required  for  cyl. 


84.8232  or  nearly  85  feet  of  fillet  required 
for  cylinder. 

N".  B. — By  taking  the  taper  off  one  end  of  the  fillet,  and  putting 
it  to  the  other  end,  nearly  b  feet  of  fillet  will  be  saved;  conse- 
quently 80  feet  of  the  above  fillet  will  be  sufficient  to  cover  a 
cylinder  of  the  above  dimensions. 

Whatever  the  width  of  the  fillet  is,  divide  the  number  of  inches 
in  the  area  of  the  cylinder,  by  the  width  of  the  fillet,  and  the 
quotient  will  be  the  number  of  inches  required  to  cover  the  cylin- 
der ;  then  deduct  the  inches  in  the  circumference  of  the  cylinder 
from  the  quotient,  and  the  remainder  will  be  the  net  length  of 
fillet  required. 

iV^.  B. —  The  circumference  of  the  cylinder  must  only  be  deducted 
when  the  taper  end  is  cut  off  the  beginning  of  the  fillet,  and  is 
intended  to  be  put  on  at  the  other  end. 


How  many  feet  of  1^  inch  fillet  will  be  required  to  cover  a 
cylinder  18  inches  diameter,  and  36  inches  wide? 


CAKDING-ENGINB. 


3.1416  equal  to  circum.  when  diam.  is  1. 
18  inches  diameter  of  cylinder. 


251328 
31416 


56.5488  circumference  of  cylinder. 
36  inches  width  of  cylinder. 

3392928 
1696464 


2035.7568 

Deduct     56.5488  circumference  of  cylinder. 


1.5)1979.2080(1319.472  inches  of  fillet  required 


29  1  ft.  =  12  in.)1319.472  inches. 
15   

 1  yd.  =  3  feet)109.956ornearlyll0ft. 

142   


70 
60 


108 
105 


30 
30 


Required  the  speed  of  the  feed-rollers  of  a  carding-engine, 
from  the  following  particulars:  — 

Revolutions  of  doffer-cylinder  a  minute  4.213. 

Wheel  on  dofier-cylinder  end,  driving  feed-roller-shaft  28  teeth. 

Wheel  on  feed-roller-shaft  (doffer  end)  28  teeth. 

W^heel  on  feed-roller-shaft,  driving  feed-rollers  13  teeth. 

Wheel  on  feed-roller  end  128  teeth. 


to  cover  the  cylinder. 


47 

45 


Or, 


135 


36.652yds.,  nearly  36f 
yards. 


CARDING-ENGINE. 


55 


iV.  B. — The  wheels  28  teeth  on  the  doffer-cylinder  end,  and  feed- 
roller-shaft,  may  be  omitted,  the  one  bemg  a  driving  and  the 
other  a  driven-wheel. 

4.213  revols.  of  doifer-cyl.  a  minute. 
13  teeth  ■wheel  on  feed-roller  shaft. 


12639 
4213 


Teeth  of  wheel  on  1  i28)54.769(.4278  revols.  of  feed-rols.  a  min. 
leed-roller-shart,  j       '  g-j^2 


356 
256 


1009 
896 


1130 
1024 


106 


If  the  diameter  of  the  fecd-rollcrs  be  1^  inches,  making  .4278 
revolutions  a  minute ;  how  many  inches  will  the  feed-rollers  tra- 
verse? 

.4278  revolutions  of  feed-rollers  a  min. 
1.5  inches  diameter  of  feed-rollers. 


21390 
4278 

.64170 

3.1416  circumference  when  diameter  is  1. 


385020 
64170 
256680 
64170 
192510 


2.015964730  or  2g'g  inches  nearly  feed-rollers 
traverse  a  minute.  • 


56 


CARDING-ENGINE, 


What  length  of  lap  will  be  required  to  supply  a  carding-engine 
1  day,  allowing  it  to  work  10  hours  (2  hours  being  allowed  for 
stripping,  grinding,  &c.),  if  the  feed-rollers  traverse  2. 01596472 
inches  a  minute? 

2.01596472  inches  feed-rols.  traverse  a  minute. 
60  minutes  =  1  hour. 


120.95788320 

10  hours  =  1  day. 

1209.57883200  inches,  or  nearly  100  feet  10 
inches  a  day. 

Required  the  weight  of  cotton  to  supply  a  carding-engine  1 
day,  the  feed-rollers  of  which  traverse  over  a  surface  equal  to 
1209.578832  inches,  there  being  24  ounces  fed  on  30  inches  of 
feed-cloth  at  lap  machine,  and  the  draught  at  lap  machine  being 
2.115. 

oz.  cotton. 

Draught  at  lap  machine,  2.115)24.000(11.347517  oz.  weight  of  30 

2115  inches  of  lap. 


2850 
2115 


7350 
6345 


10050 
8460 


15900 
14805 


10950 
10575 


3750 
2115 


16350 
14805 


1545 


J 


CARDING-ENGINE. 


5T 


Feed-cloth  at  lap  mach.  30  in.)1209.578832  in.  feed-rols.  trav. 


40.3192944  number  of  feeds. 
11.347517  oz.  weight  of  30  in. 
  of  lap. 

2822350608 
403192944 
2015964720 
2822350608 
1612771776 
1209578832 
403192944 
403192944 


4)457.5238786320048  nearly  457i  oz.,  or 

 28/(jR)s.  nearly. 

4)114.3809696580012 


28.59524241450031bs. 


Multiply  the  number  of  inches  (say  30),  on  which  24  ounces 
weight  of  cotton  is  fed  on  the  feed-cloth  at  lap  machine,  by  the 
draught  at  lap  machine,  (draught  2.115,)  and  that  sum  by  the 
number  of  ounces  in  1ft).  for  a  divisor,  and  the  number  of  inches 
the  feed-rollers  traverse  in  one  day,  or  10  hours,  by  the  number 
of  ounces  fed  on  30  inches  on  feed-cloth  at  lap  machine,  for  a 
dividend,  and  the  quotient  will  be  the  pounds  weight  required  to 
supply  the  engine. 

2.115  draught  at  the  lap  machine. 

30  inches  length  fed  on  feed-roller. 


63.450 

16  ounces  make  one  pound. 


380700 
63450 


5 


1015.200  divisor. 


58 


CARDING-ENGINE. 


1209.578832  inches  of  lap  required  a  day. 

24  oz.  weight  fed  on  30  inches  of  feed- 
 cloth  at  lap  machine. 

4838315328 
2419157664 


1015.2)29029.891968(28.5952  pounds  a  day. 

20304  16  ounces=  1  pound. 


87258  35712 
81216  5952 


60429  9.5232  oz. 

50760  4  qrs.  =  l  oz. 


96691  2.0928  qrs. 
91368 


53239 
50760 

24796 
20304 


4492  • 

iV".  B. — The  iveight  of  cotton  required  to  supply  a  preparation, 
must  he  according  to  the  number  of  carding-engines.  The 
weight  consumed  by  one  carding-engine,  multiplied  by  the 
number  of  carding-engines  in  the  preparation,  will  give  the 
weight  of  cotton  required. 

What  number  of  revolutions  will  the  doffer-cylinder  of  a  card- 
ing-engine make,  for  the  feed-rollers  1,  if  the  wheels  on  the 
doffer-cylinder  end  and  feed-roller-shaft  be  the  same  ;  and  on  the 
other  end  of  feed-roller-shaft,  a  wheel  with  13  teeth,  working 
into  a  wheel  128  teeth  on  feed-roller  end  ? 
Teeth  of  wheel  on  feed-shaft,  13)128(9.846  revols.  of  dolfer-cyl.  for 

117         feed-rollers  1. 

110 

104  80 
  78 


CARDING-BNGINE. 


59 


The  speed  of  the  lap-rollers  at  carding-engine  is  required  from 
the  following  particulars  : — 

Revolutions  of  feed-rollers  a  minute,  .4278 ;  wheel  on  feed- 
roller  end  17  teeth,  working  into  a  wheel  84  teeth  on  stud,  which 
works  into  a  wheel  46  teeth  on  lap-roller. 

.4278  revolutions  of  feed-rollers. 
17  teeth  wheel  on  feed-rollers. 


29946 
4278 


46)7.2726(.1581  revols.  of  lap-rollers  a  min, 
46 


267 
230 


Teeth  of  wheel  on 
lap-roller, 


372 
368 


46 
46 


•  If  the  lap-roller  makes  .1581  revolutions  a  minute,  and  be  3f 
inches  diameter ;  what  number  of  inches  will  it  traverse  ? 
.1581  x3.75=.592875x  3.1416=1.8625761,  or  rather  more 
than  l.hl  inches,  lap-roller  traverses  a  minute. 

If  the  feed-rollers  traverse  2.01596472  inches  a  minute,  and 
the  lap-rollers  1.862576  inches;  what  draught  is  there  between 
the  feed-rollers  and  lap-rollers  ? 

1.862576  in.)2.01596472(1.082  draught  between  lap-rollers, 
1862576  and  feed-rollers. 


15838872 
14900608 


4382640 
3725152 


657488 


60 


CARDING-ENGINE. 


OR, 

xhe  draught  between  the  feed-rollers  and  lap-rollers  is  required 
from  the  following  particulars  : — 

Wheel  on  end  of  feed-rollers  17  teeth,  working  into  stud-wheel 
84  teeth,  which  works  into  wheel  46  teeth  on  the  end  of  lap- 
rollers  ? 

Diameter  of  feed-rollers,  IJ  inches. 
Diameter  of  lap-rollers,  3|  inches. 

3.75  inches  diameter  of  lap-rollers. 
17  teeth  in  wheel  on  feed-rollers. 


2625 
375 


63.75  divisor. 


1.5  inches  diameter  of  feed-rollers. 
46  teeth  wheel  on  lap-rollers. 

90 
60 


63.75)69.00(1.0823  draught  between  lap-rollers  and 
63.75  feed-rollers. 


52500 
51000 


15000 
12750 


22500 
19125 


3375 

Required  the  draught  between  the  feed-rollers  and  lap-follers, 
from  the  following  particulars: — 

Revolution  of  feed-rollers  a  minute,  .4278. 
Revolution  of  lap-rollers  a  minute,  .1581, 
Diameter  of  feed-rollers,  1.5  inches. 
Diameter  of  lap-rollers,  3.75  inches. 


1 


CARDING-ENGINE. 


61 


.1581  revolution  of  lap-rollers  a  minute. 
3.75  inches  diameter  of  lap-rollers. 


7905 
11067 
4743 


5.92875  divisor. 


.4278  revolution  of  feed-rollers  a  minute. 
1.5  inches  diameter  of  feed-rollers. 


21390 
4278 


5.92875)6.41700(1.082  draught  between  feed-rollers 
592875  and  lap-rollers. 


4882500 
4743000 


1395000 
1185750 


209250 

What  weight  of  cotton  will  be  required  to  supply  a  carding- 
engine  1  day,  or  10  hours,  according  to  the  following  particu- 
lars ? 

Weight  fed  on  30  inches  of  feed-cloth  at  lap  machine,  24  ounces. 

Draught  at  lap  machine  2.115. 

Lap-roller  traverses  1.862576  inches  a  minute. 

60  minutes  1  hour. 


111.754560 

10  hours  =  1  day. 


1  foot  =  12  in. )1117. 545600  inches  a  day,  lap-rol.  traverses. 


93.1288  feet  a  day,  lap-roller  traverses. 


CAEDING-ENGINE. 


93.1288  feet  of  lap  required  a  day. 

24  oz.  weight  fed  on  2J  feet,  or  30  inches  of 
  feed-cloth  at  lap  machine. 

3725152 
1862576 


2235.0912  dividend. 


2.115  draught  at  lap  machine. 

2.5  feet,  or  30  in.  feed-cloth  at  lap  machine. 


10575 
4230 


5.2875 

16  ounces  =  1  pound. 


317250 
52875 


84.6000  divisor. 


84.6)2235.0912(26  6i  weight  of  cotton  required, 
1692  to  supply  a  carding-engine 
  1  day,  or  10  hours. 

5430 

5076 


354 

16  ounces  1  pound. 


2124 
354 


84.6)5664(6  oz. 
5076 


588 
4 


84.6)2352(2  qrs. 
1692 


CARDING-ENGINB. 


63 


iV.  B. — If  there  had  been  no  draught  between  the  feed-rollers  and 
lap-rollers,  the  iveight  of  cotton  required  would  have  been  28 
pounds  9|  ounces. 

The  speed  of  the  calender-rollers,  or  delivering-balls,  is  re- 
quired from  the  following  particulars : — 
Revolutions  of  doffer-cylinder  a  minute  4.213, 
Wheel  on  doffer-cylinder  end  130  teeth,  working  carrying- 
wheels,  which  works  into  a  wheel  of  28  teeth  on  delivering-ball- 
shaft. 

4,213  revolutions  of  doffer-cylinder  a  min. 
130  teeth  wheel  on  doffer-cylinder. 

126390 
4213 

Teeth  of  wheel  ^  

on  cal.  ball-  >  28)547.690(19.56  revolutions  of  delivering-halls 
shaft,  j      28  a  minute. 


267 
252 


156 
140 


169 
168 


1 

Required  the  speed  of  the  calender-rollers,  or  delivering-balls, 
from  the  following  particulars  : — 

Revolutions  of  main  cylinder  a  minute,  108.92. 
Wheel  on  axis  of  main  cylinder,  22  teeth. 
Wheel  on  stud,  140  teeth. 
Wheel  on  stud,  32  teeth. 

Wheel  on  doffer-cylinder  end,  130  teeth. — (Working  carriers.) 
Wheel  on  delivering-ball-shaft,  28  teeth. 

108.92  revolutions  of  main  cylinder  a  minute. 
22  teeth  wheel  on  axis  of  main  cylinder. 

21784 
21784 


2396,24 


* 


64 


CARDING-ENGINE. 


2396.24 

32  teeth  wheel  on  stud. 


479248 
718872 


76679.68  dividend. 


140  teeth  wheel  on  stud. 
28  teeth  wheel  on  delivering-ball-shaft. 


1120 

280 


3920  divisor. 


Divisor.  Dividend. 

3920)76679.68(19.56  revols.  of  delivering-balls  a 
3920  minute. 


37479 
35280 


21996 
19600 


23968 
23520 


448 

If  the  calender-rollers,  or  delivering-balls,  make  19.56  revo- 
lutions a  minute,  what  number  of  inches,  feet,  and  yards  will  it 
traverse,  if  their  diameters  be  3|  inches? 

3.1416  circumference  when  the  diam.  is  1. 
3.875  diameter  of  delivering-balls. 

157080 
219912 
251328 
94248 


12.1737000 


CAKDING-BNGINE.  '  65. 

12.1737000  _  vJ-";^ 

19.56  revols.  of  delivering-balls  a  minute. 


730422 
608685 
1095633 
121737 


1  ft.  =  12  in. )238. 117572  inches,  delivering-balls  traverse  a  min. 

1  yd.  =  3  ft.  )19. 843131  feet,  delivering-balls  traverse  a  min. 

6.614377  yards,  delivering-balls  traverse  a  min. 

Or,  6  yds.  1  ft.  10^  in.  nearly,  the  delivering-balls  traverse  a  min. 

The  speed  of  the  licker-in  is  required  from  the  following  par- 
ticulars :  — 

Revolutions  of  main  cylinder  a  minute  108.92. 
Diameter  of  pulley  on  cylinder,  14  inches. 
Diameter  of  pulley  on  licker-in,  7  inches. 

108.92  revols.  of  main  cyl.  a  minute. 
14  inches  diameter  of  pulley. 

43568 
10892 

Inches  diam.  of  pul. 
on  licker-in, 

217.84  revolutions  of  licker-in  a  min. 

JV.  5. —  The  only  utility  of  a  licker-in  is  the  preservation  of  the 
cards  on  the  main  cylinder,  and  whilst  many  approve  of  them, 
more  disapprove  of  them. 

The  speed  of  the  crank  is  required  from  the  following  par- 
ticulars : — 

Revolutions  of  main  cylinder  a  minute,  108.92. 

Diameter  of  pulley  on  cylinder  for  driving  crank-shaft,  16  inches. 

Diameter  of  pulley  on  crank-shaft,  7  inches. 


7)1524.88 


66 


CAKDING-ENGINB. 


108.92  revols.  of  main  cyl.  a  minute. 
16  inches  diam.  of  pulley. 

65352 
10892 


Inches- diam.  of  pul.  )  7)174972 


on  crank-shaft, 

248.96  or  nearly  249  revolutions  of 
crank-shaft  a  minute. 
Required  the  draught  of  a  carding-engine  from  the  following 
particulars ; — 

Lap-rollers  at  carding-engine  traverse  1.862576  inches  a  minute. 
Calender-rollers,  or  delivering-balls,  traverse  238.117572  inches 
a  minute. 

1.862576)238.117572(127.843  draught  of  carding-engine. 
1862576 


5185997 
3725152 


14608452 
13038032 


15704200 
14900608 


8035920 
7450304 


5856160 
5587728 


268432 

Required  the  draught  of  a  carding-engine  from  the  following 
particulars : — 

Wheel  on  calender  or  delivering-ball-shaft,  28  teeth. 
Wheel  on  doffer-cylinder  end,  130  teeth. 
Wheel  on  feed-roller-shaft,  13  teeth. 
Wheel  on  feed-rollers,  128  teeth. 

Wheel  on  feed-roller  end  for  driving  lap-rollers,  17  teeth. 
Wheel  on  lap-roller  end,  46  teeth. 
Diameter  of  calender  or  delivering-balls,  3.875  inches. 
Diameter  of  lap-rollers,  3.75  inches. 


CARDINQ-BNGINE. 


67 


JSf.B. —  The  carrying,  or  connecting  wheels  are  omitted,  as  in 
former  examples. 

28  teeth  wheel  on  delivering-ball-shaft. 
13  teeth  wheel  on  feed-roller-shaft. 


84 
28 


364 

17  teeth  wheel  on  feed-roller  end,  driving  lap- 

  rollers. 

2548 
364 


6188 

3.75  inches  diameter  of  lap-rollers. 


30940 
43316 
18564 


23205.00  divisor. 

130  teeth  wheel  on  doffer-cylinder. 
128  teeth  wheel  on  feed-rollers. 


3840 
128 


16640 

46  teeth  wheel  on  end  of  lap-roller. 


99840 
66560 


765440 

3.875  diameter  of  delivering-balls. 


3827200 
5358080 
6123520 
2296320 


2966080.000  dividend. 


68 


CARDING-ENGINB. 


23205)2966080.000(127.8  draught  of  carding-engine. 
23205 


64558 
46410 


181480 
162435 


190450 
185640 


4810 

If  one  preparation  in  the  card-room  requires  8  carding-engines, 
and  each  carding-engine  delivers  238.117572  inches  of  carding  a 
minute ;  what  length  -will  the  whole  preparation  of  carding-en- 
gines deliver  in  one  day,  allowing  them  to  work  10  hours? 

238.117572  in.  of  carding  delivered  a  min.  (1  engine). 
60  minutes  1  hour. 


14287.054320  inches  delivered  an  hour.    (1  engine.) 
10  hours  equal  to  1  day. 

142870.543200  inches  delivered  a  day.    (1  engine.) 

8  carding-engines,  one  preparation. 

inches.  

1  ft.  =  12)1 142964.345600  inches  of  carding  delivered  a  day  from 

  1  preparation. 

1  yd. =3  ft.)95247.0288  feet  of  carding  a  day  from  1  preparation. 

31749.0096  yds.  of  carding  a  day  from  1  preparation. 

What  length  of  lap  will  be  required  to  supply  8  carding-en- 
gines 1  day,  allowing  them  to  produce  1142964.3456  inches  of 
carding,  and  the  draught  at  the  carding-engine  to  be  128? 


CARDING-ENGINE. 


69 


Inches  of  carding. 
Draught  at  card.  en.  128)1142964.3456(8929.4  inches  of  lap  re- 

1024  quired. 


1189 
1152 


376 
256 


1204 
1152 


523 
512 


11 

How  many  weighings  of  cotton  must  be  fed  on  the  lap  machine, 
(each  weighing  fed  on  30  inches  of  feed-cloth,)  to  produce  8929.4 
inches  of  lap,  allowing  the  draught  at  lap  machine  to  be  2.115; 
and  what  weight  of  cotton  will  it  require,  allowing  each  weighing 
to  be  24  ounces? 

2.115  draught  at  lap  machine. 
30  inches  length  of  feed. 


63.450  in.  of  lap  each  weighing  produces. 

63.45)8929.4(140.731,  nearly  140f  weighings  of  cotton 
6345  required  a  day. 


25844 
25380 


46400 
44415 


19850 
19035 


8150 
6345 


1805 


70 


CARBING-ENGINE. 


140.731  number  of  weighings  of  cotton  required  a 
24  oz.  weight  of  one  weighing.  [day. 


562924 
281462 


.  , .  )  4)3377.544 
1  pound  IS  (   

16  oz.  844.386 

211.0965  pounds,  or  211  pounds  1^  oz.  weight  of 

  16  oz.  1  pound.  [cotton  required  a 

  day  for  1  prepa- 

5790  ration. 
965 


1.5440 

4  qrs. 

2.1760 


The  foregoing  examples  are  considered  sufficient,  because  what- 
ever principle  may  be  considered  best,  the  calculations  must  be 
made  in  the  same  way ;  the  consumption  and  production,  whether 
single  and  double  carding,  or  for  coarse  or  fine  spinning,  may  be 
ascertained  Avith  the  least  trouble  and  greatest  accuracy  by  a 
strict  adherence  to  the  rules  and  examples  illustrated. 

PARTICULARS  OF  A  CARDING-ENGINE. 

Speed  of  main-cylinder  a  minute  108.92  revolutions. 
Speed  of  doffer-cylinder  a  minute  4.213  revolutions. 
Speed  of  lap-rollers  a  minute  0.1581  revolutions. 
Speed  of  feed-rollers  a  minute  0.4278  revolutions. 
Speed  of  licker-in  a  minute  217.84  revolutions. 
Speed  of  delivering-balls  a  minute  19.56  revolutions. 
Speed  of  crank  a  minute  248,96  revolutions. 
Diameter  of  main-cylinder  37  inches,  traversing  12657.77  inches 
a  minute. 

Diameter  of  doffer-cylinder  18  inches,  traversing  288.24  inches 
a  minute. 

Diameter  of  licker-in  9  inches,  traversing  6159.29  inches  a 
minute. 


DRAWING-FRAME. 


71 


Diameter  of  lap-rollers  3|-  inches,  traversing  1.862576  inches  a 
minute. 

Diameter  of  feed-rollers  IJ  inches,  traversing  2.016  inches  a 
minute. 

Diameter  of  delivering-balls  3|  inches,  traversing  238.117572 

inches  a  minute. 
Diameter  of  pulley  on  main-cylinder  14  inches. 
Diameter  of  pulley  on  main-cylinder  for  crank  16  inches. 
Diameter  of  pulley  on  crank-shaft  7  inches. 
Diameter  of  pulley  for  driving  licker-in  14  inches. 
Diameter  of  pulley  on  licker-in  7  inches. 
Crank  half  radius  1|  inches,  or  3f  inches  sweep. 
Draught  between  lap-rollers  and  feed-rollers  1.08. 
Total  draught  at  carding-engine  128  nearly. 
Weight  of  lap  required  to  supply  a  carding-engine  1  day,  or  10 

hours  26  pounds  6|  ounces. 
Length  of  carding  delivered  per  engine  a  day  142870|  inches. 
Length  of  lap  consumed  by  1  carding-engine  a  day  1117-i  inches. 


DRAWING-FRAME. 
FIRST  HEAD. 

The  shaft  under  the  drawing-frame  for  driving  drawing-boxes, 
makes  163.38  revolutions  a  minute. — Drums  on  shaft  are  12 
inches  diameter. — Pulleys  on  the  front  rollers  are  7  inches  di- 
ameter;  the  speed  of  the  front  roller  is  required. 

163.38  revols.  of  shaft  a  minute. 

12  inches  diam.  of  drums  on  shaft. 


Inches  diam  of pul.)g  9gQ_5Q 
on  front  roller,        ^  '  


326.76  revolutions  of  front  roller  a  min. 


If  the  front  roller  of  a  drawing-frame  makes  326.76  revolutions 
a  minute,  and  its  diameter  be  1|  inches;  what  will  it  traverse? 

326.76  revolutions  of  front  roller  a  minute. 
1.125  inches  diameter  of  front  roller. 


163380 
65352 
32676 
32676 


367.60500 


72 


DRAWING-FRAME. 


367.60500 

3.1416  circumference  when  the  diameter  is  1. 


2205630 
367605 
1470420 
367605 
1102815 


1154.8678680  nearly  1155  inches,  front  roller  tra- 
verses a  minute. 

The  speed  of  shaft  under  rollers,  for  driving  middle  and  back 
rollers,  is  required  from  the  following  particulars : — 
Front  roller  makes  326,76  revolutions  a  minute. 
Wheel  on  front  roller  for  driving  wheel  on  shaft  15  teeth. 
Wheel  on  shaft  under-rollers  for  driving  middle  and  back  rollers, 

104  teeth. 

326.76  revolutions  of  front  roller  a  minute. 
15  teeth  wheel  on  front  roller. 


163380 
32676 

Teeth  of  wheen  

on  shaft  under  >  104)4901.40(47.128  revols.  of  shaft  under  rols. 
rollers,  )  416 


741 

728 


184 
104 


300 
208 


920 
832 


88 


■■I 


DRAWING-FRAME. 


73 


The  speed  of  the  middle  roller  is  required  from  the  following 
particulars: — 

Revolutions  of  shaft  under  rollers  47.128  a  minute. 
Wheel  on  shaft  for  driving  middle  roller  90  teeth. 
Wheel  on  middle  roller  33  teeth. 

47.128  revolutions  of  shaft  under  rollers. 
90  teeth  wheel  on  do.         [a  min. 


Teethofwheelon)  33  4241.520(128.53  revolutions  of  middle 
mid.  rol.,  V     ''oo  ^  n  •  ^ 

'  66  roller  a  minute. 


94 
66 

281 
264 

175 

165 

102 

99 

3 

If  the  middle  roller  makes  128.53  revolutions  a  minute,  and 
its  diameter  be  1^  inches;  what  will  it  traverse? 

128.53  revolutions  of  middle  roller  a  minute. 
1.125  inches  diameter  of  roller. 


64265 
25706 
12853 
12853 

144.59625 

3.1416  circumference  when  the  diameter  is  1. 


86757750 
14459625 
67838500 
14459625 

43378875  454.263579000  inches,  middle  roller 
 —  traverses  a  minute. 


74 


DRAWING-FRAME. 


The  draught  between  the  middle  and  front  roller  is  required, 
from  the  following  particulars: — 

Front  roller  traverses  1154.867868  inches  a  minute. 
Middle  roller  traverses  454.26358  inches  a  minute. 

454.26358)1154.867868(2.542  draught  between  middle  and 
90852716  front  roller. 


246340708 
227131790 


192089180 
181705432 


103887480 
90852716- 


12984764 

The  speed  of  the  back  roller  is  required,  from  the  following 
particulars: — 

Revolutions  of  shaft  under  rollers,  47.128  a  minute. 
Wheel  on  shaft  for  delivering  back  roller,  68  teeth. 
Wheel  on  back  roller,  56  teeth. 

47.128  revols.  of  shaft  under  rols.  a  min. 
68  teeth  wheel  on  shaft. 


377024 
282768 

Teeth  of  wheel  )  56)3204.704(57.22685  revolutions  of  back  roL 
on  DacJc  roller,  )        ^80  a  minute. 

  384 


404  336 

392  •  

  480 

127  448 

112   

  320 

150  280 
112   


DRAWINa-FRAME.  75 

If  the  back  roller  makes  57.22585  revolutions  a  minute,  and 
its  diameter  be      inches;  what  will  it  traverse? 

57.22685  revols.  of  back  roller  a  minute. 
1.125  inches  diam.  of  back  roller. 


28613425 
11445370 
5722685 
5722685 


64.38020625 

3.1416  circumference  when  the  diam.  is  1. 


38628123750 
6438020625 
25752082500 
6438020625 
19314061875 


202.256855955000,  or  202J  inches,  back  roller  tra- 
verses a  minute. 
The  draught  between  the  back  and  middle  roller  is  required, 
from  the  following  particulars  : — 

Middle  roller  traverses  454.26358  inches  a  minute. 
Back  roller  traverses  202.25685  inches  a  minute. 
202.25685)454.26358(2.24597  draught  between  back  and 
40451370  middle  roller. 


49749880 
40451370 


92985100 
80902740 


120823600 
101128425 


196951750 
182031165 


149205850 
141579795 


7620055 


76 


DRAWING-FRAME. 


JSf.  B. —  The  total  draught  of  any  machine,  zvhere  fJiere  are  inter- 
mediate draughts,  may  be  found  hy  multiplying  the  draughts 
respectively  into  each  other,  the  sum  of  which  will  be  the  total 
draught. 

The  draught  may  also  be  found  by  the  wheels,  as  will  appear 
hereafter. 

The  speed  of  the  calender-rollers,  or  delivering-balls,  is  re- 
quired from  the  following  particulars: — 

Front  roller  makes  326.76  revolutions  a  minute. 

Wheel  on  front  roller  38  teeth,  working  into  carr-ying-wheels. 

Wheel  on  calender,  or  delivering-ball-shaft,  100  teeth. 

326.76  revols.  of  front  roller  a  min. 
38  teeth  wheel  on  front  roller. 


261408 
98028 


24.1688  revolutions  of  calender,  or 
delivering-balls  a  minute. 

The  draught  between  the  front  roller  and  calender-rollers,  or 
delivering-balls,  is  required  from  the  following  particulars: — 
Front  roller  traverses  1155  inches  a  minute. 
Calender,  or  delivering-balls  trav.  1170.266  inches  a  minute. 

1155)1170.266(1.013  draught  between  front  roller 
1155  and  delivering-balls. 

1526 
1155 

3716 
3465 

251 


DRAWING-FRAME. 


77 


If  the  calender,  or  delivering-balls  make  24.1688  revolutions 
a  minute,  and  their  diameters  be  3  inches ;  what  will  they  tra- 
verse ? 

124.1688  revols.  of  delivering-balls  a  minute. 
3  inches  diameter  of  delivering-balls. 

372.5064 

3.1416  circumference  when  the  diam,  is  1. 


22350384 
3725064 
14900256 
3725064 
11175192 


1170.26610624  inches,  calender-rollers,  or  deliver- 
ing-balls traverse  a  minute. 

The  draught  at  the  first  head  of  a  drawing-frame  is  required, 
from  the  following  particulars: — 

Back  roller  makes  57.22685  revolutions  a  minute. 
Calender,  or  delivering-balls,  make  124.1688  revols.  a  min. 
Diameter  of  back  roller  IJ  inch,  or  1.125  inch. 
Delivering-balls  3  inches  in  diameter. 

57.22685  revolutions  of  back  roller  a  minute. 
1.125  diameter  of  back  roller. 


28613425 
11445370 
5722685 
5722685 


64.38020625  divisor. 

124.1688  revolutions  of  delivering-balls. 

3  inches  diam.  of  delivering-balls. 


372.5064  dividend. 


78 


DRAWING-FRAME. 


64.38)372.5064(5.786  draught  at  first  head  of  drawing- 
32190  frame. 


50606 
45066 


55404 
51504 


39000 
38628 


372 

The  draught  at  the  first  head  of  a  drawing-frame  is  required 
from  the  following  particulars  : — 

Calender,  or  delivering-ball,  traverses  1170.2661  inches  a  minute. 
Back  roller  traverses  202.2568  inches  a  minute. 

202.2568)1170.2661(5.786  draught  at  first  head  of  drawing. 
10112840 


15898210 
14157976 


17402340 
16180544 


12217960 
12135408 


82552 

The  draught  at  the  first  head  of  drawing  is  required  from  the 
following  particulars : — 
/    Wheel  on  front  roller  15  teeth,  working  into  wheel  104  teeth  on 

shaft  under  rollers. 
Wheel  on  the  other  end  of  shaft  under  rollers  68  teeth,  working 

into  wheel  on  back  roller  56  teeth. 
Wheel  on  calender,  or  delivering-ball-shaft,  100  teeth,  driven  by 

carrier-wheels  from  wheel  on  front  roller,  38  teeth. 
Diameter  of  back  rollers  1^  inch,  or  1.125  inch. 
Diameter  of  calender,  or  delivering-balls  3  inches. 


DRAWING-FRAME.  79 

100  teeth  wheel  on  delivering-ball-shaft. 
15  teeth  wheel  on  front  roller. 


1500 

68  teeth  wheel  on  end  of  shaft  on  the  rols. 


12000 
9000 


102000 

1.125  inch  diameter  of  back  rollers. 


510000 
204000 
1122000 


114750.000  divisor. 


38  teeth  wheel  on  front  roller,  driving  deliv.-ball-shaft. 
104  teeth  wheel  on  shaft  under  roller. 


152 

380 


3952 

56  teeth  wheel  on  "back  roller. 


23712 
19760 


221312 

3  inches,  diameter  of  delivering-balls. 


14750)663936(5.786  nearly,  draught  at  first  head  of  drawing- 
573750  frame. 


901860 
803250 


986100 
918000 


681000 

688500— nearly- 


80 


DRAWING-FRAME. 


What  length  of  carding  •will  it  require  to  supply  the  first  head 
of  a  drawing-frame,  having  2  pair  of  calender,  or  delivering- 
balls  in  front,  and  6  ends  of  carding  put  up  at  back  to  each 
pair  of  calender,  or  delivering-balls,  the  back  roller  traversing 
202.256856  inches  a  minute? 

202.256856  or  rather  more  than  202J  inches. 

12  ends  of  carding  to  2  pair  of  balls. 

2427.082272 

60  minutes  1  hour. 


145624.936320  inches  an  hour  required. 

If  there  be  8  carding-engines  to  a  preparation,  producing 
1142964  inches  a  day,  how  long  will  it  require  the  first  head  of 
a  drawing-frame  to  work,  to  consume  what  the  carding-engines 
produce,  allowing  the  first  head  of  drawing-frame  to  consume 
145625  inches  an  hour? 

145625)1142964(7.8486  hours. 

1019375         60  minutes  1  hour. 


1235890  50.9160,  or  7  hours  51  min.  nearly. 
1165000 


708900 
582500 


1264000 
1165000 


990000 
873750 


116250 

iV.  B. — It  will  require  the  first  head  of  a  drawing-frame  to  work 

7  hours  51  minutes  successively,  to  consume  the  production  of 

8  carding-engines,  according  to  the  ttvo  foregoing  examples. 

The  consumption  and  production  of  any  piece  of  machinery 
will  be  ascertained  in  the  same  way ;  therefore  it  will  not  be  re- 
peated. 


DRAWINQ-FBAME. 


81 


What  weight  of  cotton  will  it  require  to  be  fed  on  the  lap  ma- 
chine to  produce  1142964  inches  of  carding  a  day  (which  is 
required  to  supply  the  first  head  of  drawings),  allowing  24  ounces 
of  cotton  to  be  fed  on  30  inches  of  feed-cloth  at  the  lap  machine, 
and  the  draught  at  the  carding-engine  to  be  127.8,  and  the 
draught  at  lap  machine  2.115  ? 

Multiply  the  draughts  together,  and  that  product  by  the  num- 
ber of  inches  of  feed-cloth  that  your  weight  of  cotton  is  fed  on 
at  lap  machine,  for  a  divisor,  and  the  number  of  inches  of  carding 
required  to  supply  your  drawing-frame,  by  the  weight  fed  on  the 
given  number  of  inches  of  feed-cloth  at  lap  machine,  for  a  divi- 
dend, and  the  quotient  will  be  the  weight  in  ounces  required. 

127.8  draught  at  carding-engine. 

2.115  draught  at  lap  machine. 


6390 
1278 
1278 
2556 


270.2970 

30  inches  length  of  feed-cloth  at  lap 

 ■   machine. 

8108.9100  divisor. 


142964  inches  of  carding  required. 

24  ounces,  weight  fed  on  feed-cloth   at  lap 

  machine. 

4571856 
2285928 


8108.91)27431136(3382.8  ounces,  or  rather  more  than  211 
2432673  pounds  8|-  oz.  weight  of  cotton  re- 
 quired  to  be  fed  on  the  lap  machine. 

3104406 

2432673 


6717330 
6487128 

  6802380 

2302020  6487128 

1621782   

  315252 


82 


DRAWING-FRAME. 


DRAWING-FRAME. 
SECOND  HEAD, 

The  front  rollers  of  the  diiferent  heads  of  a  drawing-frame  are 
generally  of  the  same  speed,  and  the  only  difference  is  the 
draught  between  the  rollers. 

If  the  front  roller  makes  326.76  revolutions  a  minute,  the 
revolution  of  the  middle  roller  is  required,  from  the  following 
particulars : — 

Wheel  on  end  of  front  roller,  for  driving-shaft  under  rollers,  14 
teeth. 

Wheel  on  end  of  shaft  under  rollers,  104  teeth. 
Wheel  on  end  of  shaft  under  rollers,  driving  middle  roller,  90 
teeth. 

Wheel  on  middle  roller,  33  teeth. 

104  teeth  wheel  on  shaft  under  rollers. 
33  teeth  wheel  on  middle  roller. 


312 
312 


3432  divisor. 


326.76  revolutions  of  front  roller  a  minute. 
14  teeth  wheel  on  front  roller. 


130704 
32676 


4574.64 

90  teeth  wheel  on  shaft  under  rollers. 


3432)411717.60(119.9643,  or  nearly  120  revolutions. 


3432  which  middle  roller  makes 

  a  min. 

6851  22080 
3432  20592 


34197  14880 
30888  13728 


33096  11520 
30888  10296 


22080  1224 


4 


DRAWINa-FRAME. 


83 


If  the  middle  roller  at  second  head  of  drawing  makes 
119.9643  revolutions  a  minute,  what  will  it  traverse,  if  the  di- 
ameter be  1^  inch  ? 

119.9643  revolutions  of  middle  roller  a  min. 
1.125= It  inch  diameter  of  roller. 


5998215 
2399286 
13196073 


134.9598375 

3.1416  circumference  when  diameter  is  1. 


8097590250 
1349598375 
5398393500 
1349598375 
4048795125 


423.98982549000,  or  nearly  424  inches,  the  middle 
roller  traverses  a  minute. 

If  the  front  roller  of  the  second  head  of  drawing  traverses 
1154.867868  inches,  and  the  middle  roller  traverses  423.989825 
inches  per  minute,  what  draught  is  there  between  the  middle  and 
front  rollers  ? 

423.989825)1154.867868(2.72  draught  between  middle  and  front 
847979650  rols. 


3068882180 
2967928775 


1009534050 
847979650 


161554400 

Required  the  draught  between  the  middle  and  front  rollers  of 
the  second  head  of  drawing,  from  the  following  particulars : — 
Front  roller  makes  326.76  revolutions  a  minute. 
Middle  roller  makes  119.96  revolutions  a  minute. 


84 


DRAWING-FRAME. 


119.96)326.76(2.72  draught  between  the  middle  and  front 
23992         rollers,  second  head  of  drawing. 


86840 
83972 


28680 
23992 


4688 

The  speed  of  back  roller  at  second  head  of  drawing  is  required, 
from  the  following  particulars  : — 
Speed  of  front  roller,  326.76  revolutions  a  minute. 
Wheel  on  end  of  front  roller  for  driving-shaft  under  rollers,  14 

teeth. 

"Wheel  on  end  of  shaft  under  rollers,  104  teeth. 

Wheel  on  end  of  shaft  under  rollers,  driving  back  roller,  68  teeth. 

Wheel  on  end  of  back  roller,  56  teeth. 

104  teeth  wheel  of  shaft  under  roller. 
56  teeth  wheel  of  back  roller. 


624 
520 


5824  divisor. 


326.76  revolutions  of  front  roller  a  minute. 
14  teeth  wheel  on  end  of  front  roller. 


130704 
32676 


4574.64 

68  teeth  wheel  on  shaft  under  rollers. 


3659712 
2744784 


311075.52  dividend. 


DRAWING-FRAME. 


85 


5824)311075,52(53.412  revolutions  of  back  roller  a  min. 
29120 


19875 
17472 


24035 
23296 


7392 
5824 


15680 
11648 


4032 

If  the  back  roller  at  the  second  head  of  drawing  makes  53.412 
revolutions  a  minute,  and  its  diameter  be  IJ  inch,  what  will  it 
traverse  ? 

63.412  revolutions  of  back  roller  a  minute. 
1.125  =  IJ  inch  diameter  of  do. 

267060 
106824 
687532 


60.088500 

3.1416  circumference  when  the  diameter  is  1, 


3605310 
600885 

2403540 

600885 
1802655 


188.77403160  inches,  the  back  roller  traverses  a  min. 

The  draught  between  the  back  and  middle  rollers,  at  the  second 
head  of  drawing,  is  required  from  the  following  particulars;— 
Middle  roller  traverses  424  inches  a  minute. 
Back  roller  traverses  188.774  inches  a  minute. 


86 


DRAWING-FRAME. 


188.774)424.000(2.246  draught  between  middle 
377548  and  back  rols.  2d  head 

 of  drawing. 

464520 
377548 


869720 
755096 


1146240 
1132644 


13596 

The  draught  between  the  back  and  front  roller  is  required, 
from  the  following  particulars  : — 

Front  roller  traverses  1154.867868  inches  a  minute. 
Back  roller  traverses  188.774  inches  a  minute. 

188.774)1154.867868(6.117  draught  between  the 
1132644  back  and  front  rols., 

 2d  head  of  drawing. 

222238 
188774 


334646 
188774 


1458728 
1321418 


137310 

The  total  draught  at  the  second  head  of  drawing  is  required, 
from  the  following  particulars: — 

Wheel  on  calender  or  delivering-balls'-shaft,  100  teeth. 
AVheel  on  front  roller,  38  teeth. 

Wheel  on  front  roller,  working  shaft  under  front  rollers,  14 
teeth. 

Wheel  on  shaft  under  rollers,  104  teeth. 

Wheel  on  shaft  under  rollers,  68  teeth,  working  into  a  wheel 

on  back  rollers,  56  teeth. 
Diameter  of  calender  or  delivering-balls,  3  inches. 
Diameter  of  back  roller,  IJ  inch,  or  1.125  inch. 


DRAWING-FRAME. 


87 


Multiply  the  number  of  teeth  in  the  driving-wheels  together, 
respectively,  and  that  product  by  the  diameter  of  the  back  roller, 
for  a  divisor,  and  the  number  of  teeth  in  the  driven-wheels  to- 
gether, and  that  product  by  the  diameter  of  the  calender,  or 
delivering-balls,  for  a  dividend,  and  the  quotient  will  be  the  real 
or  total  draught,  as  in  the  following  example: — 

100  teeth  wheel  on  delivering-ball-shaft. 
14  tth.  wheel  on  front  roL,  driving-shaft  under 

  rollers. 

1400 

68  teeth  wheel  on  shaft  under  rollers. 


11200 
8400 


95200 

9  or  li  inch  diameter  of  back  roller. 


856800  divisor. 

38  teeth  wheel  on  front  roller. 
104  teeth  wheel  on  shaft  under  rollers. 


152 
380 


3952 

56  teeth  wheel  on  back  roller. 


23712 
19760 


221312 

24  or  y  =  3  inches,  diam.  of  deliv.-balls. 

885248 
442624 


5311488 


88 


DRAWING-FKAME. 


856800)5311488(6.199,  or  6.2  nearly,  draught  between 
5140800  back  roller  and  delivering-balls. 


1706880 
856800 


8500800 
7711200 


7896000 
7711200 


184800 

If  the  third,  or  last  head  of  drawing  be  same  as  the  second 
head,  what  will  the  total  draught  at  the  three  heads  of  drawing 
be,  and  what  doubling  will  there  be,  allowing  6  ends  to  be  put 
up  against  each  pair  of  calender,  or  delivering-balls,  at  each  head 
of  drawing? 

5.786  draught  at  first  head  of  drawing. 
6.199  draught  at  second  head  of  drawing. 

52074 
62074 
5786 
34716 

35.867414 

6.199  draught  at  third  head  of  drawing. 


322806726 
322806726 
35867414 
215204484 


222.342099386  rather  more  than  222/^,  total 
draught  at  the  three  heads  of 
drawing. 


-J 


DRAWING-FRAME. 


89 


DOUBLING. 

6  ends  of  carding,  first  head  of  drawing-frame. 
6  ends  of  drawing,  second  head  of  drawing-frame. 

36 

6  ends  of  drawing,  third  head  of  drawing-frame. 

216  total  doubling  at  drawing-frame. 

B. — The  above  doubling  is  small,  considering  the  quantity  of 
doubling  at  many  places  ;  however,  that  may  be  arranged  ac- 
cording to  the  opinion  of  managers,  cjx. 

If  two  pairs  of  calender,  or  delivering-balls,  at  the  first  head 
of  drawing,  traverse  1120.266  inches  each  pair  a  minute;  what 
length  of  drawing  will  they  produce  in  7.8476  hours,  or  7  hours 
51  minutes? 

1120.266  in.,  delivering-balls  traverse  a  min. 
2  pairs  at  each  head  of  drawing. 

2240..532 

7.8476  hours. 


13443192 
15683724 
8962128 
17924256 
15683724 


17582.7989232 

60  minutes  1  hour. 


1  ft.  =  12  in.)1054967.9353920  inches  produced  in  7.8476  hours. 

1  yard=3  ft.)87913. 994616  feet  produced  in  7.8476  hours. 

29304.664872  yards  produced  in  7.8476  hours. 

If  the  back  roller  at  the  second  head  of  drawing  traverses 
188.774  inches  a  minute,  and  12  ends  be  put  up;  i.  e.,  6  ends  to 
each  pair  of  delivering-balls;  what  time  must  it  work  to  consume 
1054968  inches,  which  the  first  head  of  drawing  produces  ? 


90 


DRAWING-FRAME. 


188.774  inches,  back  roller  traverses  a  minute. 
12  ends,  i.  e.,  6  to  each  pair  of  deliv.-balls. 


2265,288  inches  consumed  a  minute. 

2265.288)1054908.0(465.71  minutes,  or  7  hours  45  minutes 

9061152  42|  seconds,  the  second  head 

  must  work,  to  consume  what 

14885280  the  first  head  produces. 
13591728 


12935520 
11326440 

10090800 
15857016 

2337840 
2265288 


72552 

If  2  pairs  of  delivering-balls  in  front  of  the  first  head  of  draw- 
ing, traverse  1170.266  inches  each  a  minute;  what  length  will 
they  produce  if  they  work  successively  7  hours  51  minutes,  or 
7.8476  hours? 

1170.266  inches,  delivering-balls  traverse  a  min. 

2  pairs  of  deliv.-balls  traverse  in  first  head. 


2340.532 

60  minutes  1  hour. 


140431.920 

7.8476  hours. 


84259152 
98302344 
56172768 
112345536 
98302344 


1102053.535392  inches,  2  pairs  of  delivering-balls  at  first 
head  of  drawing  produces  in  7.8476  hours,  or  7  hours  51  min. 


DRAWING-FRAME. 


91 


If  12  ends  be  put  up  n,t  the  second  head  of  drawing,  that  is, 
6  ends  to  each  pair  of  delivering-balls,  and  the  back  roller  tra- 
verses 188.774  inches  a  minute;  what  time  must  the  second  head 
of  drawing  work,  to  consume  what  the  first  head  produces,  say 
1102053.5  inches? 

188.774  inches  back  roller  traverses  a  minute. 
12  ends. 

2265.288  divisor. 

2265.288)1102053.5(486.5  minutes  nearly,  or  8  hours 
9061152  61  minutes. 


19593830 
18122304 


14715260 
13591728 


11235320 
11326440— nearly. 

It  requires  8  hours  6J  minutes  for  the  second  head  of  drawing 
to  work,  to  consume  what  the  first  head  produces. 

iV.  B. —  The  consumption  and  production  of  the  third  head  of 
drawing  will  he  the  same  as  the  second  head. 


PARTICULARS  OF  A  DRAWING-FRAME. 

First  head,  front  roller,  326.76  revolutions  a  minute. 

Middle  roller,  128.53  revolutions  a  minute. 
Back  roller,  57.226  revolutions  a  minute. 
Delivering-balls,  124.168  revolutions  a  minute. 
Diameter  of  rollers,  1|^  inch. 
Diameter  of  delivering-balls,  3  inches. 
Draught  between  back  and  middle  rollers,  2.246. 
Draught  betvy-een  middle  and  front  rollers,  2.542. 
Draught  between  front  roller  and  delivering-balls, 
1.013. 

Total  draught  at  the  first  head  of  drawing,  5.786. 


92  TUBE-FRAME. 

Second  head,  front  roller,  326.76  revolutions  a  minute. 

Middle  roller,  120  revolutions  a  minute. 
Back  roller,  53.412  revolutions  a  minute. 
Delivering-balls,  124.168  revolutions  a  minute. 
Diameter  of  rollers,  1^  inch. 
Diameter  of  delivering-balls,  3  inches. 
Draught  between  back  and  middle  roller,  2.246. 
Draught  between  middle  and  front  roller,  2721. 
Total  draught  at  the  second  head  of  drawing,  6.123- 

i\r.  B. —  The  third  head  of  drawing  is  the  same  as  the  second  head. 

First  head,  back  roller  traverses  202.256  inches  a  minute. 


Delivering-balls  traverse  1170.266  inches  a  minute. 
Back  roller  consumes  1142964  inches,  or  211R)S.  8| 

oz.  in  7  hours  51  minutes. 
Delivering-balls  produce  1102053  inches,  or  211ibs. 

8f  oz.  in  7  hours  51  minutes. 

Second  and  third  head  back  rollers  traverse  188.774  inches  a 
minute. 

Delivering-balls  traverse  1170.266  inches  a  minute. 
Back  rollers  consume  1102053  inches,  or  211ibs.  8| 

oz.  in  8  hours  6J  minutes. 
Delivering-balls  produce  1102603  inches,  or  211ibs. 

8|  oz.  in  8  hours  6J  minutes. 

iV.  B. —  The  above  weights  of  draiving  are  the  gross  weight  of 
cotton;  the  net  weight  will  be  according  to  its  proportionate 
size,  or  girt,  in  any  operation,  as  will  be  shown  hereafter. 


TUBE-FRAME. 

The  tube-frame  is  well  calculated  for  coarse  and  medium  yarns. 

SPEEDS,  DRAUGHTS,  ETC.,  OF  THE  TUBE-FRAME. 

Speed  of  shaft  for  driving-frame,  143  revolutions  a  minute. 
Diameter  of  drum  on  said  shaft,  30  inches. 
Diameter  of  pulley  on  frame,  9f,  or  9.75  inches. 


d 


TUBE-FRAME. 


93 


143  revolutions  of  shaft  a  minute. 
30  inches,  diameter  of  drum  on  shaft. 


Diam.  of  pulley  9.75  in. )4290.00(440  revolutions  a  minute  of 
3900  front  rollers,  second  head. 


3900 
3900 

N.B. —  There  are  2  sets  or  tiers  of  rollers  to  some  of  these 
frames;  the  hack  or  receiving-rollers  are  called  the  first  head^ 
and  the  front  or  delivering-rollers  the  second  head. 

The  speed  of  the  middle  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  400. 
Wheel  on  front  rollers  21  teeth,  working  into  stud-wheel  42 
teeth. 

Wheel  on  same  stud  30  teeth,  working  into  wheel  32  teeth 
on  the  end  of  middle  rollers. 

440  revolutions  of  front  roller  a  minute. 
21  teeth  wheel  on  front  roller. 


440 
880 


9240 

30  teeth  wheel  on  stud. 


277200  dividend. 

42  teeth  wheel  on  stud. 

32  teeth  wheel  on  middle  roller. 


84 
126 


1344  divisor. 


94 


TUBE-FRAME. 


1344)277200(206.25,  or  206^  revols.  of  mid.  rols,  a  min. 
2688 


8400 
8064 


3360 
2688 


6720 
6720 

The  speed  of  the  back  rollers  is  required  from  the  following 
particulars: — 

Revolutions  of  front  rollers  a  minute,  440. 
Wheel  on  front  rollers  23  teeth,  working  into  wheel  44  teeth  on 
stud;  on  same  stud  there  is  a  wheel  20  teeth,  working  into 
wheel  41  teeth  on  back  rollers. 

44  teeth  wheel  on  stud. 

41  teeth  wheel  on  back  roller. 


44 
176 


1804  divisor. 

440  revolutions  of  front  roller  a  minute. 
23  teeth  wheel  on  front  roller. 


1320 

880  / 


10120 

20  teeth  wheel  on  stud- 


202400  dividend. 


I 


TUBE-FRAME. 


95 


1804)202400(112.195  revolutions  of  back  roller  a  minute. 
1804 


2200 
1804 


3960 
3608 


3520 
1804 


17160 
16236 


9240 
9020 


220 

The  speed  of  the  front  rollers  at  the  first  head  is  required  from 
the  following  particulars  : — 

Revolutions  of  back  roller,  second  head,  a  minute,  112.195. 
Wheel  on  back  roller,  second  head  41  teeth,  working  into  car- 
rying-wheel 41  teeth  on  stud,  which  works  into  wheel  46  teeth 
on  front  roller,  first  head. 

112.195  revols.  of  back  roL,  2d  head,  a  min. 
41  teeth  wheel  on  back  rol.,  2d  head. 


112195 
448780 
Teeth  of  wheel  )   

on  front  rols.  [  46)4599.995(99.9,  or  100  revols.  nearly,  front 
first  head,       )      414  rols.  first  head,  a  min. 


459 
414 


459 
414 


45 


96 


TUBE-FRAME. 


The  speed  of  the  middle  rollers  at  the  first  head  is  required 
from  the  following  particulars  : — 
Revolutions  of  front  rollers  a  minute,  100. 
Wheel  on  front  rollers  21  teeth,  working  into  a  wheel  on  stud  42 

teeth  ;  wheel  30  teeth  on  same  stud,  works  into  wheel  32  teeth 

on  middle  roller. 

42  teeth  wheel  on  stud. 

32  teeth  wheel  on  middle  roller. 


84 
126 


1344  divisor. 


100  revolutions  of  front  roller  a  minute. 
21  teeth  wheel  on  it. 


2100 

30  teeth  wheel  on  stud. 


1344)63000(46.875  revols.  of  mid.  rol.  a  minute. 

5376 


9240 
8064 


11760 
10752 


10080 
9408 


6720 
6720 

The  speed  of  the  back  roller  at  the  first  head  is  required  from 
the  following  particulars : — 
Revolutions  of  front  rollers  a  minute,  100. 
Wheel  on  front  rollers  27  teeth,  working  into  stud  wheel  58  teeth ; 

on  same  stud  there  is  a  wheel  17  teeth,  working  into  wheel  58 

teeth  on  back  rollers. 


TUBE-FRAME. 


97 


58  teeth  wheel  on  stud. 

58  teeth  wheel  on  back  rollers. 


464 
290 


3364  divisor. 


100  revolutions  of  front  rollers  a  minute. 
27  teeth  wheel  on  front  rollers. 


2700 

17  teeth  in  wheel  on  stud. 


18900 
2700 


3364)45900(13.644  revolutions  of  back  roller  a  minute. 
3364 


12260 
10092 


21680 
20184 


14960 
13456 


15040 
13456 


1584 

iV.  B. —  When  toorldng  the  speeds  of  rollers,  the  driven-ioheels 
onultiplied  into  each  other  will  be  the  divisor. 

The  speed  of  the  friction  rollers  is  required  from  the  following 
particulars: — 

Eevolutions  of  front  rollers,  second  head,  a  minute,  440. 

Wheel  on  front  rollers  28  teeth,  working  into  wheel  59  teeth  on 
bevil-shaft ;  on  the  other  end  of  bevil-shaft  there  is  a  wheel 
32  teeth,  working  into  wheel  50  teeth  on  friction-roller-shaft. 


98 


TUBE-FRAME. 


59  teeth  wheel  on  bevil-shaft. 
50  teeth  wheel  on  friction-roller-shaft. 


2950  divisor. 


440  revolutions  of  front  rollers  a  minute. 
28  teeth  wheel  on  front  rollers. 


3520 
880 


12320 

32  teeth  wheel  on  bevil-shaft. 


24640 
36960 


2950)394240(133.64  revolutions  of  friction-rols.  a  minute. 

2950 


9924 

8850 


10740 

8850 


18900 
17700 


12000 
11800 


200 

The  speed  of  the  tubes  is  required  from  the  following  par- 
ticulars : — 

Revolutions  of  pulley-shaft  a  minute,  440. 
Diameter  of  pulley  on  said  shaft,  18  inches. 
Diameter  of  tubes,  |  inch,  or  .875  inch. 

440  revolutions  of  pulley-shaft  a  min. 
18  inches,  diam.  of  pul.  on  said  shaft. 

3520 
440 

  7920 


TUBE-FRAME. 


99 


Inches  diam.  of  tubes. 875)7920(9051.428  revols.  of  tubes  a  min. 

7875 


4500 
4375 


1250 
875 


3750 
3500 


2500 
1750 


7500 
7000 


500 

The  draught  between  the  back  and  middle  rollers  at  the  first 
head  is  required  from  the  following  particulars  : — 

Revolutions  of  back  rollers  a  minute,  13.644. 
Revolutions  of  middle  rollers  a  minute,  46.875. 
Diameters  of  back  and  middle  rollers,  1  inch. 

13.644)46.875(3.435  draught  between  back  and 
40932  middle  rollers. 


59430 
64576 


48540 
40932 


76080 
68220 


7860 

The  draught  between  the  middle  and  front  rollers  is  required 
from  the  following  particulars: — 

Revolutions  of  middle  rollers  a  minute,  46.875. 
Revolutions  of  front  rollers  a  minute,  100. 


100 


TUBE-FRAME. 


Diameter  of  middle  rollers,  1  inch. 
Diameter  of  front  rollers,  1|-  inch,  or  1.125  inch. 
100  revolutions  of  front  rollers  a  minute. 
1.125  inch  diameter  of  do. 


46.875)112.500(2.4  draught  between  middle  and  front  rols. 
93750 


187500 
187500 

The  total  draught  at  the  first  head  is  required  from  the  fol- 
lowing particulars  : — 

Draught  between  back  and  middle  rollers,  3.435. 
Draught  between  middle  and  front  rollers,  2.4. 
3.435 
2.4 


13740 
6870 


8.2440  nearly  8J  total  draught,  first  head. 

The  draught  between  the  front  roller  first  head,  and  the  back 
roller  second  head,  is  required  from  the  following  particulars: — 
Revolutions  of  front  rollers  first  head  a  minute,  100. 
Revolutions  of  back  rollers  second  head  a  minute,  112.195. 
Diameter  of  front  rollers  first  head,  1|  inch,  or  1.125  inch. 
Diameter  of  back  rollers  second  head,  1  inch. 

100  revols.  of  front  roller  a  min.  first  head. 
1.125  inches  diameter  of  front  roller. 


112.500  divisor. 


112.5)112.195(0.997  diminution  of  draught  between 
10125  the  two  heads  of  rollers. 


10945 
10125 


8200 
7875 


325 


TUBE-FRAME. 


101 


N.  B.—On  account  of  the  distance  between  the  first  and  second 
head  of  rollers,  a  draught  would  he  injurious. 

The  draught  between  the  back  and  middle  rollers  at  the  second 
head  is  required  from  the  following  particulars : — 

Revolutions  of  back  rollers  a  minute,  112.195. 
Ilevolutions  of  middle  rollers  a  minute,  206.25. 
Diameters  of  middle  and  back  rollers,  1  inch. 

112.195)206.250(1.8383  draught  between  back  and 
112195  middle  rollers  second  head. 


910550 
897560 


429900 
336585 


933150 
897560 


355900 
336585 


19815 

The  draught  between  the  middle  and  front  rollers  at  the  secondl 
head  is  required  from  the  following  particulars : — 

Revolutions  of  middle  rollers  a  minute,  206.25. 
Revolutions  of  front  rollers  a  minute,  440. 
Diameter  of  middle  roller,  1  inch. 
Diameter  of  front  roller,  1\  inch,  or  1.125  inch. 
1.125  inch,  diameter  of  front  rollers. 

440  revolutions  of  front  rollers  a  minute. 


45000 
4500 


206.25)495000(2.4  draught  between  mid.  and  front  rols. 
41250 


82500 
82500 


102 


TUBE-FRAME. 


The  draught  between  the  front  rollers  and  friction-rollers  is 
required  from  the  following  particulars : — 

Revolutions  of  front  rollers  a  minute,  440. 
Revolutions  of  friction-rollers  a  minute,  133.64. 
Diameter  of  friction-rollers,  4  inches. 
Diameter  of  front  rollers,  1^  inch,  or  1.125  inch. 

440  revolutions  of  front  rollers. 
1.125  inches  diameter  of  front  rollers. 


45000 
4500 


495.000  divisor. 


133.64  revolutions  of  friction-rollers. 

4  inches  diameter  of  friction-rollers. 


495)534.56(1.08  nearly,  draught  between  front 
495  rollers  and  friction-rollers. 


3956 

3960— nearly. 

The  total  draught  at  the  second  head  is  required  from  the 
foUov/ing  particulars :  (including  draught  between  front  rollers 
and  friction-rollers.) 

Draught  between  back  and  middle  rollers,  1.8383. 
Draught  between  middle  and  front  rollers,  2.4. 
Draught  between  front  and  friction-rollers,  1.08. 

1.8383  draught  between  back  and  middle  rollers. 
2.4  draught  between  middle  and  front  rols. 


73532 
36766 


4.41192  draught  between  back  and  front  rollers. 
1.08  di'aught  between  front  and  friction-rols. 


8529536 
4411920 


4.7648736  total  draught  between  back  rollers  second 
head,  and  friction-rollers. 


TUBE-FRAME. 


103 


The  total  draught  at  a  tube-frame  is  required  from  the  fol- 
lowing particulars : — 

Draught  at  first  head,  8.244 
Draught  at  second  head,  and  friction-rollers,  4,764 

32976 
49464 
67708 
32976 


39.274416  total  draught. 

The  total  draught  at  a  tube-frame  is  required  from  the  fol- 
lowing particulars : — 

Wheel  on  friction-roller-shaft  50  teeth,  working  into 

Wheel  on  bevil-shaft  32  teeth. 

Wheel  on  top  of  shaft  59  teeth,  working  into 

Wheel  on  front  roller  second  head  28  teeth. 

Wheel  on  front  roller  second  head  23  teeth,  working  into 

Wheel  on  stud  44  teeth. 

Wheel  on  same  stud  20  teeth,  working  into 

Wheel  on  back  roller  second  head  41  teeth,  working  into  a 

Wheel  on  stud  41  teeth,  which  works  into 

Wheel  on  front  roller  first  head  46  teeth. 

Wheel  on  front  roller  27  teeth,  working  into 

Wheel  on  stud  58  teeth. 

Wheel  on  same  stud  17  teeth,  working  into 

Wheel  on  back  roller  first  head  58  teeth. 

Diameter  of  friction-pulley,  4  inches. 

Diameter  of  back  roller  fii'st  head,  1  inch. 

50  teeth  wheel  on  friction-roller-shaft. 

59  teeth  wheel  on  top  of  bevil-shaft. 

2950 

23  teeth  wheel  on  front  roller  second  head. 


8850 
~  5900 


67850 

20  teeth  wheel  on  second  head. 


1357000 


TUBE-FRAME. 

1357000 

41  teeth  wheel  on  stud  between  the  heads. 


1357000 
5428000 


55637000 

27  teeth  wheel  on  front  roller  first  head. 


389459000 
111274000 


1502199000 

17  teeth  wheel  on  stud  first  head. 


10515393000 
1502199000 


25537383000  divisor. 


32  teeth  wheel  on  bevil-shaft. 

28  teeth  wheel  on  front  roller  second  head. 


256 
64 


896 

44  teeth  wheel  on  stud  second  head. 


8584 
3584 


39424 

41  teeth  wheel  on  back  roller. 


39424 
157696 


1616384 

46  teeth  wheel  on  front  roller. 


9698304 
6465536 

  74353664 


TUBE-FRAME, 


105 


74353664 

58  teeth  wheel  on  stud. 


594829312 
371768320 


4312512512 

58 


34500100096 
21562562560 


250125725696 

4  inches  diameter  of  friction-pulley. 

25537383.000)1000502902.784(39.178  total  draught  between 

76612149  back  rols.  first  head  and 

  friction-rols. 

234381412 
229836447 


45449657 
25537383 


199122748 
178761681 


203610674 
204299064— nearly. 

B. —  The  small  difference  between  this  and  the  other  method 
arises  from  the  decimal  farts;  however,  the  last  method. is  the 
most  accurate. 

If  the  back  rollers  at  the  first  head  make  13.644  revolutions  a 
minute,  and  their  diameter  be  1  inch ;  what  will  they  traverse  ? 


teeth  wheel  on  back  roller  first 

head. 


8 


lOG 


TUBE-FRAME. 


13.644 

3.1416  circumference  when  the  diam.  is  1. 


81864 
13644 
54576 
13644 
40932 


42.8639904  nearly  43  inches,  back  rollers  tra- 
verse at  first  head  a  minute. 

If  22  drawings  be  put  up  at  the  back  of  the  tube-frame,  what 
length  will  it  consume  a  minute,  if  the  back  rollers  traverse 
42.864  inches  a  minute? 

42.864  inches  back  rollers  traverse  a  minute. 
22  drawings  put  up  at  the  back  of  the  frame. 

85728 
85728 


943.008  inches  of  drawing  consumed  a  minute. 

What  time  must  a  tube-frame  work  to  consume  551027  inches 
of  drawing,  if  it  consumes  943  inches  a  minute.'' 

943)551027(584  minutes,  or  9  hours,  44  minutes 
4715  tube-frame  must  work  successive- 

  ly,  to  consume  what  the  last  head 

7952         of  drawing  produces. 
7544 


4087 
3772 


315 

N.B. —  There  are  1102054  me/tes  of  drawing  produced  at  the 
last  head  of  draivings;  but  on  account  of  the  drawing  being 
put  up  double  at  the  back  of  the  frame,  only  one-half  the  length 
is  reckoned  for  consumption,  i.  e.  551027  inches. 


t 


TUBE-FRAME. 


107 


If  the  front  roller  of  a  tube-frame  makes  440  revolutions  a 
minute,  and  the  diameter  of  the  rollers  be  IJ  inch;  what  length 
of  roving  will  the  frame  produce,  if  it  contains  22  tubes,  and 
works  9  hours,  44  minutes  successively  in  1  day? 

1.125  diameter  of  front  rollers  =  IJ  inch. 
3.1416  circumference  when  the  diameter  is  1. 


6750 
1125 
4500 
1125 
3375 


85.343000 

440  revolutions  of  front  rollers  a  minute. 


1413720 
141372 


1555.0920  inches,  each  tube  receives  a  minute. 
22  drawings  put  up  at  back  of  the  frame. 


3110184 
3110184 


34212.024  inches,  or  950  yards,  12  inches,  or  1  hank 
110  yards,  12  inches,  tube-frame  produces  a  minute,  i.  e.,  if  there 
be  no  draught  betwixt  the  front  rollers  and  the  friction-rollers. 

34212  inches  of  roving  produced  a  minute. 
584  minutes  =  9  hours,  44  minutes. 


136848 
273696 
171060 


C  6)19979808  inches  of  roving  produced. 

lyd.  =  36in.^   

t  6)3329968 


554994.66 


108 


TUBE-FRAME. 


Yards  in  a  hank,  840)554994.66(660.7  hanks,  or  660  hanks,  4 
5040  leas,  114  yards. 


5099 
5040 


5946 
6880 


66 

If  660  hanks  of  roving  weighs  211JK)S.  what  hank  roving  will 
it  be? 

211.5)660.7(3.124,  or  3|  hank  roving  nearly. 
6345 


2620 
2115 


5050 
4230 


8200 

8460— nearly. 

iV.  B. — If  the  211J?5s.  of  cotton  had  been  carried  through  all  the 
different  processes  of  carding,  drawing,  and  roving,  without 
any  loss,  it  would  have  produced  a  roving  equal  to  3.124  hanks 
to  the  pound,  but  as  loss  is  sustained  in  the  different  processes, 
that  loss  can  only  be  accurately  ascertained  by  working  the 
zveight  of  cotton  consumed  regularly  through  all  the  processes, 
and  ascertaining  the  net  weight  of  roving  which  will  be  accord- 
ing to  the  following  example. 

If  the  roving  be  3.75  hanks  to  the  pound;  what  will  be  the 
net  weight  of  660.7  hanks,  and  what  weight  will  be  lost  at  the 
different  processes,  allowing  211Jl]bs.  to  have  been  consumed  at 
the  carding-engines  ? 


TUBE-FRAME.  ,109 

Hank  roving,  3.75)660.7(176.186ibs.  weight  of  roving  producM-^-- 
375  from  211^ibs.  of  cotton. 


2857 
2625 


2320 
2250 


700 
375 


3250 
3000 


2500 
2250 


250 

211.5ibg.  of  cotton  consumed  at  1  prep,  a  day. 
176,1  BGlbs.  of  roving  produced  at  1  prep,  a  day. 

35.314ibs.  loss  sustained  in  working  through  the 
different  processes,  which  is  nearly  2|-  ounces  to  the  pound. 

If  a  tube-frame  produces  176.18Gibs.  of  roving  a  day;  what 
weight  of  roving  will  it  produce  in  6  days? 

176.186K)S.  of  roving  produced  a  day. 
6  days 


1057.116ibs.,  or  1057R)S.  If  oz.  a  week. 
16  oz.  =  ISb. 


696 
116 


1.856  oz. 

4  qrs.  =  1  oz. 


3.424  qrs. 


110 


TUBE-FRAME. 


PARTICULARS  OF  A  TUBE-FRAME. 

Revolutions  of  friction-rollers  a  minute,  133.64. 
Revolutions  of  front  rollers  second  head  a  minute,  440. 
Revolutions  of  middle  rollers  second  head  a  minute,  206.25. 
Revolutions  of  back  rollers  second  head  a  minute,  112.195. 
Revolutions  of  front  rollers  first  head  a  minute,  100. 
Revolutions  of  middle  rollers  first  head  a  minute,  46.875. 
Revolutions  of  back  rollers  first  head  a  minute,  18.644. 
Revolutions  of  tubes  a  minute,  9051.428. 
Diameter  of  friction-rollers,  4  inches. 
Diameter  of  tubes,  |  inch. 

Diameter  of  front  rollers  first  and  second  head,  Ij  inch. 
Diameter  of  middle  and  back  rollers  first  and  second  head,  1  inch. 
Tube  traverses  a  minute,  24881  inches. 
Friction-rollers  traverse  a  minute,  1679  inches. 
Front  rollers  second  head  traverse  a  minute,  1555  inches. 
Middle  rollers  second  head  traverse  a  minute,  648  inches. 
Back  rollers  second  head  traverse  a  minute,  352.5  inches. 
Front  rollers  first  head  traverse  a  minute,  353.4  inches. 
Middle  rollers  first  head  traverse  a  minute,  147.24  inches. 
Back  rollers  first  head  traverse  a  minute,  42.85  inches. 

DRAUGHTS. 

Draught  between  back  and  middle  rollers  first  head,  3.435. 
Draught  between  middle  and  front  rollers  first  head,  2.4. 
Draught  between  front  rollers  first  head  and  back  rollers  second 
head,  0.997. 

Draught  between  back  and  middle  rollers  second  head,  1.8383. 
Draught  between  middle  and  front  rollers  second  head,  2.4. 
Draught  between  front  rollers  and  friction-rollers,  1.08. 
Total  draught  at  the  first  head,  8.244. 
Total  draught  at  the  second  head,  4.4119. 
Total  draught  at  tube-frame,  39.178. 

N.  B. —  The  consumption  and  production  is  according  to  the 
traversing  of  the  rollers,  ivhich  in  all  cases  will  be  found  hy 
multiplying  the  number  of  revolutions  of  the  rollers  by  their 
circumferences. 

The  distance  of  the  rollers  from  each  other  must  be  regulated 
according  to  the  staple  and  quality  of  cotton. 


SLABBING-FRAME. 


Ill 


SLABBING-FRAME. 

The  speed  of  the  principal,  or  main-shaft  at  slabbing-frame,  is 
required  from  the  following  particulars  ? 

Revolutions  of  shaft  a  minute  driving  slabbing-frame,  114. 
Diameter  of  drum  on  said  shaft,  16  inches. 
Diameter  of  pulley  on  frame-shaft,  15  inches. 

114  revels,  of  driving-shaft  a  minute. 
16  diameter  of  drum  on  driving-shaft. 


684 
114 


Diam.  of  pulley,  15  in.)1824(121.6  revols.  of  frame-shaft  a  min. 
15 


32 
30 


24 
15 


90 
90 

The  speed  of  the  front  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  frame-shaft  a  minute,  121.6. 

Wheel  on  said  shaft  64  teeth,  working  into  carrying-wheel  138 

teeth  on  stud,  which  works  into  a  wheel  60  teeth  on  front 

rollers. 

121.6  revols.  of  frame-shaft  a  min. 
64  teeth  wheel  on  said  shaft. 


4864 
7296 


Wheel  on  front  roller,  60  tth.)7782.4 


129.706  revols.  of  front  rols.  a  min. 

The  speed  of  the  middle  rollers  is  required  from  the  following 
particulars: — 


112 


SLABBINQ-FRAME. 


Revolutions  of  front  rollers  a  minute,  129.7. 
Wheel  on  front  rollers  24  teeth,  working  into  wheel  70  teeth  on 
stud ;  on  the  same  stud  a  wheel  25  teeth  works  into  wheel  56 
teeth  on  back  rollers ;  wheel  on  the  other  end  of  back  rollers 
30  teeth,  working  into  wheel  64  teeth  on  stud,  which  works 
into  wheel  27  teeth  on  middle  rollers. 

129.7  revolutions  of  front  rollers  a  minute. 
24  teeth  wheel  on  front  rollers. 


5188 
2594 


3112.8 

25  teeth  wheel  on  stud.  (Change  pinion.) 


155Q40 

62256 


77820.0 

30  teeth  wheel  on  back  roller. 


2334600  dividend. 

70  teeth  wheel  on  stud. 

56  teeth  wheel  on  back  rollers. 


3920 

27  teeth  wheel  on  middle  roller. 


27440 
7840 


105840  divisor. 

105840)2334600(22.0578 
211680 


217800 
211680 


612000 
529200 


revols.  of  middle  rols.  a  min. 

828000 
740880 


871200 
846720 

24480 


SLABBING-FRAME. 


113 


The  speed  of  the  back  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  129.7. 

Wheel  on  front  rollers  24  teeth,  working  into  wheel  70  teeth  on 

stud;  wheel  25  teeth  on  same  stud,  works  into  wheel  56  teeth 

on  back  rollers. 

129.7  revolutions  of  front  rollers  a  min. 
24  teeth  wheel  on  front  rollers. 


5188 
2594 


3112.8 

25  teeth  wheel  on  stud. 


155640 
62256 


77820.0  dividend. 

70  teeth  wheel  on  stud. 

56  teeth  wheel  on  back  rollers. 


3920  divisor. 

3920)77820(19.852  revolutions  of  back  rols.  a  minute. 

3920 


38620 
35280 


33400 
31360 


20400 
19600 


8000 
7840 


160 


114 


SLABBING-PRAME. 


The  traversing  of  the  front,  middle,  and  back  rollers,  are  re- 
quired from  the  three  foregoing  examples,  allowing  the  front 
rollers  to  be  Ij  inch,  and  the  middle  and  back  rollers  1  inch 
diameter. 

129.7  revolutions  of  front  rollers  a  minute. 
1.125  inches,  diameter  of  front  rollers. 


6485 
2594 
1297 
1297 


145.9125 

3.1416  circumference  when  diameter  is  1. 


8754750 
1459125 
6836500 
1459125 
4377375 


458.39871000  inches,  front  roller  traverses  a  min. 

22.0578  revolutions  of  middle  rollers  a  minute. 
3.1416  circumference  when  the  diameter  is  1. 


1323468 
220578 
882312 
220578 
661734 


69.29678448  inches,  middle  rollers  traverse  a  min. 

19.852  revolutions  of  back  rollers  a  min. 
3.1416  circum.  when  the  diameter  is  1. 


119112 
19852 
79408 
19852 
59556 


62.3670432  inches,  back  rollers  traverse  a  min. 


i 


SLABBING-FRAME. 


115 


The  draught  between  the  back  and  middle  rollers,  the  draught 
between  the  middle  and  front  rollers,  and  the  total  draught  is 
required  from  the  three  foregoing  examples? 

62.367)69.29678(1.111,  or  rather  more  than  li  draught 
62367  between  back  and  middle  rollers. 


69297 
62367 


69308 
62367 


69410 
62367 


7043 

69.2967)458.39870(6.615  draught  between  middle  and  front 
4157802  rollers. 


4261850 
4157802 


1040480 
692967 


3475130 
3464835 


10295 

62.367)458.3987(7.35  draught  between  back  and  front  rols., 
436569  or  total  draught  at  slabbing-frame. 


218297 
187101 


311960 
311835 


125 


116 


SLABBING-FRAME. 


The  draught  between  the  back  and  middle  rollers  is  required 
from  the  following  particulars  : — 

Wheel  on  back  rollers  30  teeth,  working  into  wheel  64  teeth  on 

stud,  which  works  into  wheel  27  teeth  on  middle  roller. 

Diameter  of  back  and  middle  rollers,  each  1  inch. 

rr,         J.    V    1       ( 3)30  teeth  wheel  on  back  rollers. 
Teeth  oi  wheel  on  ) 


middle  roller,  27 


9)10 


1^  draught  between  back  and  middle 

rollers. 


The  draught  between  the  middle  and  front  rollers  is  required 
from  the  following  particulars: — 

Wheel  on  front  roller  24  teeth,  working  into  wheel  70  teeth  on 
stud ;  wheel  25  teeth  on  same  stud,  working  into  wheel  56 
teeth  on  back  rollers ;  on  the  other  end  of  back  rollers,  wheel 
30  teeth  working  into  wheel  64  teeth  on  stud;  same  stud  wheel 
working  wheel  27  teeth  on  middle  rollers. 

Diameter  of  front  rollers,  1|,  or  1.125  inch. 

Diameter  of  back  rollers,  1  inch. 

DRIVma-WHEELS. 

24  teeth  wheel  on  front  rollers. 

25  teeth  wheel  on  stud  working  back  rols. 


120 

48 


600 

30  teeth  wheel  on  back  rollers. 


18000 

8,  or  1  inch  diameter  of  middle  rollers. 


44000  divisor. 

DRIVBN-WHEELS. 

70  teeth  wheel  on  stud. 

56  teeth  wheel  on  back  rollers. 


3920 


SLABBING-FRAME. 


117 


3920 

27  teeth  wheel  on  middle  rollers- 


27440 
7840 


105840 

9,  or  I  inch  diameter  of  middle  rollers. 


144000)952560(6.615  draught  between  middle  and  front 
864000  rollers. 


885600 
864000 


216000 
144000 


720000 
720000 

The  total  draught  is  required  from  the  following  particulars: — 
Wheel  on  front  rollers  24  teeth,  working  into  wheel  70  teeth  on 
stud ;  wheel  on  same  stud  25  teeth,  working  into  wheel  56 
teeth  on  back  rollers. 

Diameter  of  back  rollers,  1  inch. 

Diameter  of  front  rollers,  1^,  or  1.125  inch. 

DRIVING-WHEELS. 

24  teeth  wheel  on  front  rollers. 

25  teeth  wheel  on  stud.  (Change  pinion.) 

120 

48 


600 

8,  or  1  inch  diameter  of  back  rollers. 


4800  divisor. 


118  SLABBING-FRAME. 


DRIVEN-WHEELS. 

70  teeth  wheel  on  stud. 

56  teeth  wheel  on  back  rollers. 

3920 

9,  or  1^  inch  diameter  of  front  rollers. 


48.00 


12)352.80 
4)  29.4 


7.35  total  draught  at  slabbing-frame. 

What  length  of  drawing  will  be  required  to  supply  a  slabbing- 
frame  1  day  (allowing  it  to  work  at  the  rate  of  9  hours  suc- 
cessively), having  40  spindles,  and  the  back  rollers  traversing 
62.367  inches  a  minute  ? 

62.367  inches,  back  rollers  traverse  a  min. 
40  spindles  in  frame. 


2494.680 

9  hours  =  1  day. 


22452.120 

60  minutes  =  1  hour. 


36  in.,  1  yard,  < 


(  6)1347127.200  inches  of  drawing  required  a  day. 


(  6)224521.2 


37420.2  yards  of  drawing,  or  44  hanks,  3 
leas,  110^  yards,  required  to  supply  a  slabbing-frame  9  hours, 
or  1  day. 

What  time  must  a  slabbing-frame  with  40  spindles  work  a  day, 
to  consume  1102054  inches  of  drawing,  if  it  consumes  2494.68 
inches  a  minute? 


SLABBING-PRAME. 


119 


2494.68)1102054(441.76  minutes  or  7  hours,  21  minutes, 
997872  45  seconds,  the  slabbing-frame 

 must  work  to  consume  what  the 

1041820  last  head  of  drawings  produces. 

997872 


439480 
249468 


1900120 
174.6276 


1538440 
1496808 


41632 

If  the  front  rollers  of  a  slabbing-frame  traverse  458.4  inches 
a  minute,  and  the  diameter  of  the  rollers  be  1^  inch,  the  number 
of  spindles  40 ;  what  length  of  slabbing  will  it  produce  in  7  hours, 
21  minutes,  and  45  seconds,  or  441.76  minutes? 

458.4  inches,  rollers  traverse  a  minute. 
40  spindles  in  frame. 

18336.0  slabbing-frame  produces  a  minute. 
441.76  minutes,  or  7  hours,  21|-  minutes. 


110016 
128352 
18336 
73344 
73344 


r  6)8100111.36  inches  of  slabbing  produced  in  7 

lyd.=36in.  <   hours  21|- minutes. 

(6)1350018.56 

1  lea  =  120  yds.)225003.0933  yards  of  slabbing  produced  in  7 

 hours,  21f  minutes. 

1  hank  =  7  leas)1875. 02577  leas  of  slabbing  produced  in  7 

 hours,  21|  minutes. 

267.860822 


120 


SLABBING-FRAME. 


267.860822  hanks  of  slabbing  produced  in  7 
7  leas,  1  hank,  [hours,  21f  minutes. 


6.025755  leas. 

120  yards,  1  lea. 


3.090666  yds.  or  267  hanks,  6  leas,  3  yds. 

If  267  hanks,  6  leas,  and  3  yards,  or  267.8608  hanks  of  slab- 
bing weighs  211Jl]bs.;  what  hank  will  it  be? 

RULE — Divide  the  number  of  hanks  by  the  weight,  and  the 
quotient  will  be  the  hanks  in  one  pound. 

Sbs.  Hanks. 

211.5)267.8608(1.266  hanks  of  slabbing  in  one  pound. 
2115 


5636 
4230 


14060 
12690 


13708 
12690 


1018 

If  the  211|-  ibs.  of  cotton  had  been  carried  through  the  dif- 
ferent operations  without  waste,  according  to  the  foregoing  dou- 
blings and  draughts,  it  would  have  produced  a  slabbing  equal  to 
1.266,  or  rather  more  than  IJ  hanks  to  the  pound,  but  on  trying 
the  slabbing  I  find  it  to  be  equal  to  1.5  hanks  to  the  pound : 
what  loss  is  sustained  in  working  ? 

RULE — Divide  the  number  of  hanks  produced  by  the  hank- 
slabbing,  which,  subtracted  from  the  gross  weight  of  cotton, 
say  211JS)S.,  will  show  the  loss  sustained  in  working. 


SLABBING-FRAME. 


121 


Hanks 

Ilank-slabbing,  1.5)267.8608(178.574,  or  178ibs.  9  oz.  of  slab- 
15  bing  produced  from  211Jibs. 

  of  cotton. 

117 
105 


128 
120 


86 
75 


110 

105 


58 

60 — nearly. 

ft)s.  oz. 

211 .  .  8  gross  weight  of  cotton  fed  on  lap  machine. 
178  . .  9  net  weight  of  slabbing  produced. 

32..  15  loss  sustained  in  working.  (Flies,  strips,  &c.) 

TURNS  AN  INCH  ON  SLABBING. 

The  turns  an  inch  on  the  slabbing,  are  required  from  the  fol- 
lowing particulars: — 

Revolutions  of  frame-shaft  a  minute,  121.6. 

Wheel  on  said  shaft  90  teeth,  working  into  wheel  138  teeth  on 

stud,  which  works  into  wheel  46  teeth  on  shaft  for  driving 

spindles. 

Wheel  on  shaft  driving  spindles,  50  teeth. 
Wheel  on  spindles,  25  teeth. 

Front  rollers  traverse  458.3987,  or  nearly  458.4  inches  a  minute. 

iV".  B. —  The  wheel  138  teeth  is  a  carrying-wheel ;  there  is  another 
ivheel  138  teeth  ivhieh  is  omitted,  it  being  a  carrier  also. 


9 


SLABBING-FRAMB. 


121.6  revolutions  of  frame-shaft  a  minute. 
90  teeth  in  wheel  on  said  shaft. 


10944.0 

50  teeth  wheel  on  spindle-shaft. 


547200  dividend. . 

46  teeth  wheel  (driven)  on  spindle-shaft. 
25  teeth  wheel  on  spindles. 


230 

92 


1150  divisor. 

1150)547200(475.8  revolutions  of  spindles  a  minute. 
4600 


8720 
8050 


6700 
6750 


9500 
9200 


300 

Inches.    Revolutions  of  spindles. 

458.3987)475.8260(1.038  turns  an  inch  on  slabbing. 
4583987 


17427300 
13751961 


S6753390 
36671896 


81494 


ROVING-FRAME. 


123 


ROVING-FRAME. 

The  speed  of  the  first  propelled-shaft  of  the  roving-frame  is 
required  from  the  following  particulars : — 

Revolutions  of  shaft  driving  roving-frame  a  minute,  143. 
Diameter  of  drum  on  said  shaft,  16  inches. 
Diameter  of  pulley  on  frame-shaft,  15  inches. 

143  revolutions  of  shaft  a  minute. 
16  inches  diameter  of  drum  on  shaft. 


858 
148 


Inches  diam.  of  J^^""^^ 
pulley,  15,  , 


3)457.6 


152.533  revolutions  of  first  propelled-shaft 
at  roving-frame  a  minute. 

The  speed  of  the  front  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  frame-shaft  a  minute,  152.533. 
Wheel  on  same  shaft  54  teeth,  working  into  carrying-wheel  138 
teeth,  which  works  into  wheel  70  teeth  on  front  rollers. 

152.533  revols.  of  shaft  a  minute. 
54  teeth  wheel  on  said  shaft. 


610133 
762666 


frontM  ^^'^^      }  70)8236.800 

117.66857  revols.  of  front  rollers  a  miu. 

If  the  front  rollers  of  a  roving-frame  make  117.66857  revolu- 
tions a  minute,  and  their  diameter  be  1^,  or  1.125  inch;  what 
will  they  traverse  a  minute  ? 

117.6685  revols.  of  front  rollers  a  minute, 
1.125,  or  IJ  inch  diameter  of  front  rol. 


5883425 
2353370 
1176685 
1176685 

  132.3770625 


124 


ROVING-FRAME. 


132.3770625 

3.1416  circumference  when  diameter  is  1. 


7942623750 
1323770625 
5295082500 
1323770625 
3971311875 


415.87577955000  inches,  front  rol.  traverses  a  min. 

The  speed  of  the  middle  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  117.6685. 
Wheel  on  front  rollers  24  teeth,  working  into  wheel  70  teeth  on 
stud ;  on  same  stud  wheel  24  teeth,  works  into  wheel  60  teeth 
on  back  rollers ;  wheel  30  teeth  on  the  other  end  of  back 
rollers,  works  into  wheel  64  teeth  on  stud,  which  works  into 
wheel  24  teeth  on  middle  rollers. 

117.6685  revols.  of  front  rols.  a  min. 
24  teeth  wheel  on  do. 


4706740 
2353370 


2824.0440 

24  teeth  wheel  on  stud. 


11296176 
5648088 


67777.056 

30  teeth  wheel  on  back  rollers. 

2033311.680  dividend. 

70  teeth  wheel  on  stud. 
60  teeth  wheel  on  back  rollers. 

4200 

24  teeth  wheel  on  middle  rollers. 


16800 
8400 

  100800  divisor. 


ROVING-FRAME. 


125 


1008.00)20333.11.68(20.1717  revols.  of  mid.  rols.  a  minute. 
2016 


1731 
1008 


7231 
7056 


1756 
1008 


7488 
7056 


432 

If  the  middle  rollers  be  1  inch  diameter,  making  20.1717  re- 
volutions a  minute ;  what  will  they  traverse  ? 

20.1717  revolutions  of  middle  rollers  a  minute. 
3.1416  circumference  when  diameter  is  1. 


1210302 
201717 
806868 
201717 
605151 


63.37141272  inches,  middle  rollers  trav.  a  minute. 

The  speed  of  the  back  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  117.6685. 
Wheel  on  front  rollers  24  teeth,  working  into  wheel  70  teeth  on 
stud;  on  same  stud  wheel  24  teeth,  works  into  wheel  60  teeth 
on  back  rollers. 

117.6685  revolutions  of  front  rollers  a  minute. 
24  teeth  wheel  on  do. 


4706740 
2353370 


2824.0440 


126 


ROVING-FRAME. 


2824.0440 

24  teeth  wheel  on  stud. 


11296176 
5648088 


67777.056  dividend. 

70  teeth  wheel  on  stud. 
60  teeth  wheel  on  back  rollers. 


4200  divisor. 


42.00)677.77.056(16.137  revolutions  of  back  rollers 
42  a  minute. 


257 
252 


57 
42 


157 
126 


310 
294 


16 

If  the  back  rollers  be  1  inch  diameter,  making  16.137  revolu- 
tions a  minute ;  what  will  they  traverse  ? 

16.137  revolutions  of  back  rollers  a  minute. 
3.1416  circumference  when  diameter  is  1. 


96822 
16137 
64548 
16137 
48411 


50.6959992,  or  50/^  inches  nearly,  back  rollers 

traverse  a  minute. 


ROVING-FRAME. 


127 


The  draught  of  roving-frame  is  required  from  the  following 
particulars : — 

Wheel  on  front  rollers,  24  teeth  (driving). 
Wheel  on  stud,  70  teeth  (driven). 
Wheel  on  same  stud,  24  teeth  (driving). 
Wheel  on  back  rollers,  60  teeth  (driven). 
Diameter  of  back  rollers,  1  inch  (driving). 
Diameter  of  front  rollers,  1^  inch  (driven). 

DRIVING-WHEELS. 

24  teeth  wheel  on  front  rollers. 

24  teeth  wheel  on  stud.  (Change  pinion.) 


96 
48 


576 

8=1  inch,  diameter  of  back  rollers. 


4608  divisor. 

DRIVEN-WHEELS. 

70  teeth  wheel  on  stud. 
60  teeth  wheel  on  back  rollers. 


4200 

9,  or  1 J  inch,  diameter  of  back  rollers. 


37800  dividend. 


4608)37800(8.203 
36864 


9360 
9216 


14400 
13824 


576 

If  the  back  rollers  of  a  roving-frame  traverse  50.696  inches 
a  minute,  with  72  spindles  ;  what  length  of  slabbing  will  it  con- 


128 


ROVING-FRAME. 


sume,  allowing  the  slabbing  to  be  doubled,  or  2  ends  to  each 
spindle  ? 

50.696  inches,  back  rollers  traverse  a  minute. 
72  spindles  in  frame. 


101392 
354872 


3650.112 

2  slabbings  to  each  spindle. 

7300.224  inches,  of  slabbing  consumed  at  roving- 
frame  a  minute. 

If  1  roving-frame  consumes  7300.224  inches  of  slabbing  a 
minute ;  "what  time  must  2  roving-frames  work,  to  consume 
8100111.36  inches? 

7300.224  inches,  consumed  a  min.  by  1  frame. 
2  frames. 


Divisor,  14600.448  inches,  2  frames  consume  a  minute. 


14600.448)8100111.36(554.78  minutes,  or  9  hours,  14f  minutes, 
73002240  2  roving-frames  must  work  suc- 

 cessively,  to  consume  what  the 

79988736  slabbing-frame  produces. 

73002240 


69864960 
58401792 


114631680 
102203136 


124285440 
116803584 


7481856 

What  length  of  roving  will  2  frames,  of  72  spindles  each,  pro- 
duce in  9  hours,  14|-  minutes,  or  554.78  minutes,  if  the  front 
rollers  traverse  415.87  inches  a  minute? 


I 


ROVING-FRAME.  129 

415.87  inches  front  rollers  traverse  a  minute. 
72  spindles  in  1  frame. 


83174 
291109 


29942.64  inches  of  roving  one  frame  produced  a 
2  frames.  [minute. 


59885.28  inches  of  roving  2  frames  prod,  a  min. 
554.78  minutes,  or  9  hours,  14|  minutes. 


47908224 
41919696 
23954112 
29942640 
29942640 

33223155.6384  inches  of  roving  the  2  frames  produce 
in  554.78  minutes,  or  9  hours  14f  min. 

How  many  hanks  of  roving  are  there  in  33223155.6384 
inches? 

(0)33223155.6384  inches  of  roving. 

1  yard  is  36  in. 


6)5537192.6064 


1  hank  is  840  yards,)922865.4344(1098.6493  hanks  of  roving. 

840  7  leas  1  hank. 


8286  4.5451  leas. 

7560  120  yards  1  lea. 


7265  65.4120  yards. 

6720 

  7834 


5454  7560 
5040   


  2744 

4143  2520 

3360   

224 


3^223155.6384  inches  of  roving  will  be  1098.6493  hanks,  or  1098 
hanks,  4  leas,  and  65  yards. 


130 


ROVING-FRAME. 


If  1098  hanks,  4  leas,  and  65  yards,  or  1098.6493  hanks  of 
roving  weigh  211^  pounds;  what  hank  will  it  be? 
Pounds.  Hanks. 
211.5)1098.6493(5.194  hanks  roving. 
10575 


4114 
2115 


19999 
19035 


9643 
8460 


1183 


N.  B. — If  the  211|Z5s.  of  cotton  could  be  carried  through  all  the 
different  operations  in  the  card  room  to  the  roving  without 
ivaste,  it  zvould  produce  a  roving  equal  to  5.194  hanks  in  the 
pound  [allowing  the  doublings  and  draughts  to  be  the  same, 
as  shown  informer  examples). 

If,  on  trying  the  roving,  its  weight  is  equal  to  6.15  hanks  in 
the  pound,  what  weight  of  roving  will  there  be  in  1098.649 
hanks  ? 

Hanks.  Hanks  yarn. 

6.15)1098.649(178.64  pounds  of  roving. 
615  16  oz.  1  pound. 


4836  384 
4305  64 


5314  10.24  oz. 
4920 


3949 
3690 


2590 
2460 


130 


ROVING-FRAME. 


131 


Weight  of  cotton  fed  on  lap  machine,  211S)S.    8  oz. 
Weight  of  roving  produced,    -    -    -  178Sbs.  10}  oz. 


Loss  sustained  in  working,      -    -    .     32ft>s.  13|  oz. 

The  speed  of  the  spindles  of  roving-frame  is  required  from 
the  following  particulars: — 
Revolutions  of  frame-shaft  a  minute,  152.533. 
Wheel  on  frame-shaft  68  teeth,  working  into  carrying-wheel  138 

teeth,  which  works  into  a  wheel  52  teeth  on  spindle-shaft ; 

wheel  72  teeth  on  spindle-shaft,  works  into  wheel  18  teeth  on 

spindle. 

152.533  revolutions  of  frame-shaft  a  minute. 
68  teeth  wheel  on  frame-shaft. 


1220266 
915200 


10372.266 

72  teeth  wheel  on  spindle-shaft  for  driv- 

  ing  spindles. 

20744533 
72605866 


746803.200  dividend. 

52  teeth  wheel  on  spindle-shaft. 
18  teeth  wheel  on  spindle. 


416 

52 


936  divisor. 

936)746803.2(797.86 
6552 


9160 
8424 


7363 
6552 


revolutions  of  roving-frame 
spindles  a  minute. 

8112 
7488 


6240 
5616 


I 

132 


THROSTLE-FRAME. 


The  turns  an  inch  of  roving  are  required,  from  the  following 
particulars: — 

Revolutions  of  spindles  a  minute,  797.86. 
Front  rollers  traverse  a  minute,  316  inches. 

316)797.86(2.525  turns  an  inch  of  roving. 
632 


1658 
1580 


786 
632 


1540 

1580 — nearly. 

The  speeds  of  any  moving  power  belonging  to  machinery  may 
be  found  in  the  same  manner  as  illustrated  in  the  foregoing  ex- 
amples. 

The  construction  of  the  slabbing  and  roving-frames  differs 
materially;  every  machine-maker  having  a  method  of  his  own, 
whereby  to  work  the  different  moving  powers,  belonging  to,  and 
connected  with,  the  slabbing  and  roving-frames;  while  every 
master,  manager,  and  overlooker  generally  gives  a  preference 
to  some  particular  machine-maker. 

Improvements  in  all  kinds  of  machinery  are  continually  pro- 
gressing, but  the  system  of  calculations  remains  the  same;  there- 
fore the  system  being  well  grounded,  and  on  sure  data,  the 
improvements  possible  to  be  made  will  be  the  more  easily  arrived 
at,  and  while  theory  and  practice  are  combined  together,  it  will 
give  both  pleasure  and  satisfaction  to  the  mind. 


THROSTLE-FRAME. 

Throstles,  like  all  other  machinery,  vary  in  construction 
either  in  one  part  or  another,  and  while  some  persons  prefer  the 
patent  throstles,  of  which  there  are  several,  others  give  the  pre- 
ference to  the  common  throstle;  but  whatever  the  construction 
of  the  machine  may  be,  any  person  having  a  thorough  knowledge 
of  calculations  in  addition  to  practice,  will  be  enabled  to  form  a 
proper  estimate  of  machinery  according  to  improvements  and 
alterations  made. 


THROSTLE-FRAME, 


133 


To  produce  regular  yarns,  it  is  very  essential  to  have  good 
Avashers;  in  place  of  round  pieces  of  cloth,  many  prefer  a  strip  of 
stout  washer  cloth,  of  a  proper  width,  and  length  of  the  throstle, 
with  holes,  according  to  the  number  and  distance  of  spindles. 
The  washers,  being  stationary,  have  more  power  on  the  bobbins ; 
consequently,  the  yarns  receive  the  twist  more  regularly. 

The  speed  of  the  tin  drum,  or  cylinder  for  driving  spindles,  is 
required  from  the  following  particulars: — 
Revolutions  of  shaft  for  driving  throstles  a  minute,  153. 
Diameter  of  drum  on  said  shaft,  24  inches. 
Diameter  of  pulley  on  tin  drum,  or  cylinder-shaft  for  driving 

spindles,  10  inches. 

153  revolutions  of  shaft  a  minute. 
24  inches,  diam.  of  drum  on  shaft. 


612 

306 


Diam.  of  pulley,  10  in.  )3672 

367.2,  or  3671-  revolutions  of  tin  drum, 
or  cylinder  for  driving  spindles,  a  minute. 

If  the  tin  drum,  or  cylinder  for  driving  spindles,  makes  367.2 
revolutions  a  minute ;  what  number  of  revolutions  will  the  spin- 
dles make,  if  the  tin  drum,  or  cylinder,  be  12  inches  diameter, 
and  the  wharves  1  inch. 

367.2  revols.  of  tin  drum,  or  cylinder,  a  min. 
12  inches,  diameter  of  tin  drum. 


4406.4  revolutions  of  spindles  a  minute. 

The  revolutions  a  minute  of  the  front  rollers  are  required 

from  the  following  particulars: — 

Revolutions  of  pulley-shaft  a  minute,  367.2. 

Wheel  on  same  shaft  32  teeth,  working  into  large  stud  wheel  122 
teeth  ;  on  same  stud  a  wheel  40  teeth,  works  into  carrying- 
wheel  122  teeth,  which  works  into  wheel  54  teeth  on  front 
rollers. 


134 


THROSTLE-FRAME. 


367.2  revolutions  of  pulley-shaft  a  minute. 
32  teeth  wheel  on  shaft. 


7344 
11016 


11750.4 

40  teeth  wheel  on  stud. 


470016.0  dividend. 

122  teeth  wheel  on  stud. 
54  teeth  wheel  on  end  of  front  rollers. 


488 
610 


6588  divisor. 

6588)470016(71.344  revols.  of  front  rols.  a  min. 
46116 


8856 
6588 


22680 
19764 


29160 
26352 


28080 
26352 


1728 

If  the  front  rollers  of  a  throstle  make  71.344  revolutions  a 
minute;  what  will  they  traverse  if  they  be  1  inch  diameter? 


THROSTLE-FKAMB. 


135 


71.344  revolutions  of  front  rollers  a  min. 
3.1416  circumference  when  diameter  is  1. 


428064 
71344 

285376 

71344 
214032 


224.1343104  rather  more  than  224|-  inches,  front 
rollers  traverse  a  minute. 

If  the  front  rollers  of  a  throstle  traverse,  or  deliver  224.134 
inches  a  minute ;  how  many  hanks  a  spindle  will  be  produced  in 
1  week,  if  the  throstle  works  successively  60  hours,  thus  allow- 
ing 9  hours  for  doffing  and  other  stoppages  ? 

224.134  inches,  front  rollers  deliver  a  min. 
60  minutes,  1  hour. 


13448.040 

60  hours,  1  week. 


C  6)806882.400  inches  produced  a  spindle  a  week, 

36  inches,  1  yd.  

(6)134480.4 

1  lea  is  12.0  yds.  )2241.3.4  yards  produced  a  week. 

1  hank  is  7  leas,  )186. 77833  leas  produced  a  week. 

26.682619  hanks  produced  a  week. 
7  leas  1  hank. 


4.778333  leas. 

120  yards  1  lea. 

93.340000  yards. 

The  length  produced  a  spindle  in  60  hours,  or  1  week,  will  be 
26  hanks,  4  leas,  and  93/g  yards. 

The  speed  of  the  middle  rollers  is  required  from  the  following 
particulars : — 


13l3 


THROSTLE-FRAME. 


Revolutions  of  front  rollers  a  minute,  71.344. 
Wheel  on  front  rollers  20  teeth,  working  into  stud  wheel  90  teeth  ; 
on  the  same  stud  change  wheel  23  teeth,  works  into  wheel  46 
teeth  on  back  rollers;  on  the  other  end  of  back  rollers  there 
is  a  wheel  25  teeth,  working  into  carrying-wheel  36  teeth  on 
stud,  which  works  into  wheel  19  teeth  on  middle  rollers. 

71.344  revolutions  of  front  rollers  a  minute. 
20  teeth  wheel  on  front  roller. 


1426.880 

23  teeth  wheel.    (Change  pinion.) 


4280640 
2853760 


32818.240 

25  teeth  wheel  on  back  rollers. 


16409120 
G563648 


820456.00  dividend. 

90  teeth  wheel  on  stud. 

46  teeth  wheel  on  back  rollers. 


4140 

19  teeth  wheel  on  middle  rollers. 


37260 
4140 


78660  divisor. 

78660)820456(10.43  revolutions  of  middle  rollers  a  minute. 
78660 


338560 
314640 


239200 
235980 


3220 


TimOSTLE-FRAME. 


137 


If  the  middle  rollers  of  a  throstle  be  |  inch  diameter,  making 
10.43  revolutions  a  minute ;  what  will  they  traverse  ? 

10.43  revolutions  of  middle  rollers  a  minute. 
.75,  or  J  inch  diameter  of  middle  rollers. 


5215 
7301 


7.8225 

3.1416  circumference  when  diameter  is  1. 


469350 
78225 
312900 
78225 
234675 


24.57516600  or  rather  more  than  24J  inches,  middle 
rollers  traverse  a  minute. 

The  speed  of  the  back  rollers  of  a  throstle  is  required  from 
the  following  particulars  : — 
Revolutions  of  front  rollers  a  minute,  71.844. 
Wheel  on  front  rollers  20  teeth,  working  into  large  stud  wheel 
90  teeth ;  small  stud  wheel,  or  change  pinion  23  teeth,  work- 
ing into  wheel  46  teeth  on  back  rollers. 

71.344  revolutions  of  front  rollers  a  min. 
20  teeth  wheel  on  front  rollers. 


1426.880 

23  teeth  wheel  change  pinion. 


428064 
285376 


32818.24  dividend. 

90  teeth  wheel  on  stud. 

46  teeth  wheel  on  back  rollers. 


4140  divisor. 

10 


138 


THROSTLE-FKAME. 


4140)32818.24(7.927  revolutions  of  back  rollers  a 
28980  minute. 


88382 
37260 


11224 

8280 


29440 
28980 


460 

If  the  back  rollers  of  a  throstle  be  |  inch  diameter,  making 
7.927  revolutions  a  minute;  what  will  they  traverse? 

7.927  revols.  of  back  rollers  a  minute. 
875  or  ^  inch  diam.  of  back  roller. 


39635 
55489 
63416 


6.936125 

3.1416  circumference  when  diameter  is  1- 


41616750 
6936125 
27744500 
6926125 
20808375 


21.7905303000,  or  rather  more  than  21f  inches, 
back  rollers  traverse  a  minute. 

If  the  back  rollers  of  a  throstle  traverse  21.79  inches  a  minute, 
and  the  middle  rollers  24.575  inches  ;  what  draught  will  there  be  ? 

21.79)24.575166(1.128  draught  between  back  and 
2179  middle  rollers. 


2785 
2179 


6061  17036 

4358  17432-^nearly. 


THROSTLE-FRAME. 


139 


If  the  middle  rollers  of  a  throstle  traverse  24.575166  inches 
a  minute,  and  the  front  rollers  224.13431;  what  draught  will 
there  be  between  the  middle  and  front  rollers? 

24.575)224.13431(9.12  draught  between  middle 
221175  and  front  rollers. 


29593 
24575 


50181 
49150 


1031 

If  the  back  rollers  of  a  throstle  traverse  21.79  inches  a  minute, 
and  the  front  rollers  224.1343;  what  draught  will  there  be  be- 
tween the  front  and  back  rollers? 

21.79)224.1343(10.286  draught  between  the  back 
2179  and  front  rollers. 


6234 
4358 


18763 
17432 


13310 
13074 


236 

If  the  driving-wheels  be  20  and  23,  and  the  driven-wheels  90 
and  46,  the  diameter  of  the  front  rollers  1  inch,  and  the  back 
rollers  |  inch  ;  what  draught  Avill  there  be  ? 

DRIVING-WHEELS. 

20 
23 


460 

Back  roller  |  inch,  or  7 


3220  divisor. 


uo 


THKOSTLE-FRAME. 


DRIVEN-WHEELS. 

90 
46 


4140 

8  =  1  inch  front  rollers. 


3220)33120(10.286  nearly,  draught  in  rols. 
3220 


9200 
6440 


27600 
25760 


18400 
.  19320— nearly. 

If  one  spindle  produces  26  hanks,  4  leas,  and  93  yards,  or 
26.682G22  hanks  of  twist  a  week;  what  length  and  weight  of 
No,  30's  twist  will  6876  spindles  produce? 

26.682622  hanks  a  spindle  a  week. 
6876  spindles. 


160095733 
186778355 
213460977 
160095733 


No.  of  twist,  3.0's)18346.9.709988  hanks  of  twist  a  week. " 

6115.6569996ft)s.  of  twist  a  week. 
16  ounces  1  ib. 


39419976 
6569996 


10.5119936  ounces. 

4  qrs.  1  oz. 

2.0479744 

Length  of  twist  produced,  18346.97,  nearly  18347  hanks. 
Weight  of  twist  produced,  6115it)s.  10^  oz.  of  No.  30's  twist. 


I] 


THROSTLE-FRAME. 


141 


The  speed  of  the  mangle- wheel  is  required,  from  the  following 
particulars: — 

Revolutions  of  pulley-shaft  a  minute,  367.2. 
Wheel  on  said  shaft  32  teeth,  Avorking  into  stud-wheel  122  teeth; 
wheel  on  same  stud  G  teeth,  working  into  wheel  110  teeth 
on  mangle-wheel-shaft ;  wheel  8  teeth  on  mangle-wheel-shaft, 
working  into  mangle-wheel  82  teeth. 

122  teeth  wheel  on  stud. 
110  teeth  wheel  on  mancle-wheel-shaft. 


13420 

82  teeth  mangle-wheel. 


26840 
107360 


1100440  divisor. 

367.2  revolutions  of  pulley-shaft  a  minute. 
82  teeth  wheel  on  pulley-shaft. 


7344 
11016 

11750.4 

6  teeth  wheel  on  stud. 


70502.4 

8  teeth  wheel  on  mangle-wheel-shaft. 


1100440)564019.2(.512539,  or  rather  more  than  half  a 
5502200  revolution  of  mangle-wheel 


1379920 
1100440 

2794800 
2200880 

5939200 
5502200 


a  minute- 


  10686800 

4370000  9903960 

3301320   

  782840 


142 


THROSTLE-FRAME. 


The  speed  of  the  traverse-shaft  is  required,  from  the  following 
particulars: — 

Revolution  of  mangle- wheel  a  minute,  .512539. 
Wheel  on  mangle-wheel  21  teeth  working  racks,  which  works 
into  wheel  43  teeth  on  traverse-shaft. 

.51254  revolution  of  mangle-wheel  a  minute. 
21  teeth  on  mangle-wheel,  working  racks. 

51254 
102508 
Teeth  of  wl.  ^  

on  traverse-  V 43)10. 76384(.25,  or  rather  more  than  |-  of  a  revo- 
shaft,  J        86  lution  of  traverse-shaft  a  min. 


216 
215 


1  * 

What  will  the  traverse  move  a  minute,  according  to  the  follow- 
ing particulars: — 

Revolution  of  traverse-shaft  a  minute,  .25,  or  J. 
.Diameter  of  pulleys  on  traverse-shaft,  1^^  inch. 

3.1416  circumference  when  diameter  is  1. 
1.5,  or  IJ  inch  diameter  of  pulleys  on 

  traverse-shaft. 

157080 
31416 


4.71240 

.25  or  J  revolution  of  traverse-shaft. 


235620 
94248 


1.178100,  or  rather  more  than  IJ  inch,  tra- 
verse moves  a  minute. 

If  the  front  rollers  of  a  throstle  traverse,  or  deliver  224.135 
inches  a  minute,  and  the  spindles  make  4406.4  revolutions  a 
minute,  how  many  turns  will  there  be  in  1  inch  of  twist  ? 


I 


THROSTLE-FRAME. 


143 


Deliv.  a  min.,  224.135  in.)4406.400(19.65958  turns  an  inch  for 

224135  No.  30's  twist. 


2165050 
2017215 


1478350 
1344810 


1335400 
1120675 


2147250 
2017215 


1300350 
1120675 


1796750 
1793080 


3670 

PARTICULARS  OF  A  THROSTLE-FRAME. 

Revolutions  of  a  tin-drum,  or  cylinder  for  driving  spindles  a 

minute,  367.2. 
Revolutions  of  spindles  a  minute,  4406.4. 
Revolutions  of  front  rollers  a  minute,  71.34426. 
Revolutions  of  middle  rollers  a  minute,  10.4304. 
Revolutions  of  back  rollers  a  minute,  7.927. 
Revolution  of  mangle-wheel  a  minute,  0.51254. 
Revolution  of  traverse-shaft  a  minute,  0.25. 
Diameter  of  pulleys  on  drum,  or  cylinder-shaft,  10  inches. 
Diameter  of  drum,  or  cylinder  driving  spindles,  12  inches. 
Diameter  of  wharves,  1  inch. 
Diameter  of  front  rollers,  1  inch. 
Diameter  of  middle  rollers,  f  inch. 
Diameter  of  pulleys  on  traverse-shaft,  IJ  inch. 
Front  rollers  traverse  or  deliver  a  minute,  224.134  inches. 
Middle  rollers  traverse  a  minute,  24.57  inches. 
Back  rollers  traverse  or  consume  a  minute,  21.79  inches. 
Traverse  or  bobbin  rail  moves  a  minute,  1.17956  inches. 
Draught  between  back  and  middle  rollers,  1.2878  nearly. 


144 


MULES. 


Draught  between  middle  and  front  rollers,  9,12. 
Total  draught  in  rollers,  10.286. 
Turns  per  inch  for  30's  twist,  19.659,  or  19f  nearly. 
Hanks  per  spindle  produced,  26  hanks,  4  leas,  and  yards 
a  week  of  sixty  hours. 

MULES. 

The  speed  of  the  rim-shaft  is  required  from  the  following  par- 
ticulars : — 

Revolutions  of  shaft  for  driving  upright-shaft  in  wheel-house,  86. 
Dili  meter  of  drum  on  said  shaft,  25  inches. 
Diameter  of  pulley  on  upright-shaft  in  wheel-house,  12  inches. 
Wheel  on  foot  of  upright-shaft  in  wheel-house  68  teeth,  working 
into  wheel  45  teeth  on  rim-shaft. 

86  revolutions  of  shaft  a  minute. 
25  inches  diameter  of  drum  on  shaft. 


430 
172 


2150 

68  teeth  wheel  on  foot  of  upright-shaft 

  in  wheel-house. 

17200 
12900 


146200  dividend. 

12  inches  diameter  of  pulley  on  upright-shaft  in 
45  teeth  wheel  on  rim-shaft.  [wheel-house. 


540  divisor. 

54.0)14620.0(270.74  revolutions  of  rim-shaft  a 
108  minute. 


382 
378 

  220 

400  216 
378   


MULES. 


145 


Or  thus,  which  is  preferable  ^Yhen  it  can  be  divided  by  com- 
ponent parts: — 


9)2436.66 

270.'}  4  revolutions  of  rim-shaft  a  minute. 


The  speed  of  the  front  rollers  is  required,  from  the  following 
particulars : — 

Revolutions  of  rim-shaft  a  minute,  270.74. 

Wheel  on  rim-shaft  50  teeth,  working  into  wheel  64  teeth  on  top 
of  long  driver-shaft;  wheel  on  bottom  of  long  driver-shaft  40 
teeth,  working  into  wheel  80  teeth  on  front  rollers. 


270.74  revolutions  of  shaft  a  minute. 
50  teeth  wheel  on  shaft. 


13537.00 

40  teeth  wheel  on  bottom  of  long  driver. 


541480  dividend. 

64  teeth  wheel  on  top  of  long  driver. 
80  teeth  wheel  on  front  rollers. 


5120  divisor. 

512.0)54148.0(105.75  revolutions  of  front  rollers 
512  a  minute. 


2948 
2560 


3880 
3584 


2960 
2560 


54.0 


400 


146 


MULES. 


If  the  front  rollers  be  1  incli  diameter,  making  105.75  revolu- 
tions a  minute,  what  will  they  traverse  ? 

105.75  revolutions  of  front  rollers  a  minute. 
3.1416  circumference  when  diameter  is  1. 


63450 
10575 
42300 
10575 
31725 

332.224200,  or  332ii  inches,  front  rollers  tra- 
verse a  minute. 

The  speed  of  the  middle  rollers  is  required,  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  105.75. 

Wheel  on  front  rollers  24  teeth,  working  into  wheel  100  teeth 
on  shaft  for  driving  back  rollers ;  wheel  on  shaft  for  driving 
back  rollers  25  teeth,  working  into  wheel  50  teeth  on  back 
rollers ;  wheel  on  back  rollers  24  teeth,  working  into  carrying- 
wheel  40  teeth  on  stud,  which  works  into  wheel  21  teeth  on 
middle  rollers. 

105.75  revolutions  of  front  rollers  a  minute. 
24  teeth  wheel  on  front  roller. 


42300 
21150 


2538.00 

25  teeth  wheel  (change  pinion)  on  shaft  driving 
  back  rollers. 


12690 
5076 


63450 

24  teeth  wheel  on  back  rollers. 


253800 
126900 


1522800  dividend. 


I 


MULES. 


147 


100  teeth  wheel  on  shaft  driving  back  rollers. 
50  teeth  wheel  on  back  rollers. 


5000 

21  teeth  wheel  on  middle  rollers. 

105000  divisor. 

105.000)1522.800(14.5  revolutions  of  middle  rollers  a 
105  minute. 

472 
420 


528 
525 


3 

If  the  middle  rollers  be  |^  inch  diameter,  making  14J  revolu- 
tions a  minute;  what  will  they  traverse? 

14.5  revolutions  of  middle  rollers  a  minute. 
.875,  or  I  inch  diameter  of  rollers. 

725 
1015 
1160 


12.6875 

3.1416  circumference  when  diameter  is  1. 


761250 
126875 
507500 
126875 
380625 


39.85905000  inches,  middle  rollers  traverse  a  min. 

The  speed  of  the  back  rollers  is  required  from  the  following 
particulars: — 

Revolutions  of  middle  rollers  a  minute,  14.5  inches. 
Wheel  on  middle  roller  21  teeth,  working  into  carrying-wheel  40 
teeth  on  stud,  which  works  into  wheel  24  teeth  on  back  rollers. 


148  MULES. 


14.5  revolutions  of  middle  rollers  a  minute. 
21  teeth  wheel  on  middle  roller. 


145 
290 


Teethofwheel  >  24)304.5(12.6875  revolutions  of  back  rollers  a 
on  mid.  rols.    S       oa  ■  ^ 

'       5:4  mmute. 


64 
48 

165 
144 

210 
192 

180 
168 


120 
120 


If  the  back  rollers  be  |  inch  diameter,  making  12.6875  revo- 
lutions a  minute;  what  will  they  traverse? 

12.6875  revolutions  of  back  rollers  a  minute. 
.875,  or  \  inch  diameter  of  rollers. 


634375 
888125 
1015000 

11.1015625 

3.1416  circumference  when  diameter  is  1. 


666093750 
111015625 
444062500 
111015625 
333046875 


34.87666875000,  or  34|  inches,  back  rollers  traverse 
a  minute. 


MULES. 


149 


The  draught  between  the  back  and  middle  rollers  is  required 
from  the  following  particulars: — 

Middle  rollers  traverse  a  minute,  39.859. 
Back  rollers  traverse  a  minute,  34.876. 

34.876)39.859(1.14288  draught  between  back  and 
34876  middle  rollers. 


49830 
34876 

149540 
139504 

100360 
69752 

306080 
279008 

270720 

279008— nearly. 

The  draught  between  the  front  and  middle  rollers  is  required 
from  the  following  particulars  : — 

Front  rollers  traverse  a  minute,  332.2242  inches. 
Middle  rollers  traverse  a  minute,  39.859  inches. 
39.859)332.2242(8.3349  draught  between  front  and  mid.  rols. 
318872 


133522 
119577 


139450 
119577 

198730 
159436 

392940 
358731 


34209 


150 


MULES. 


The  draught  between  the  front  and  back  rollers  is  required 
from  the  following  particulars: — 

Front  rollers  traverse  a  minute,  332.2242  inches. 
Back  rollers  traverse  a  minute,  34.8766  inches. 

34.8766)332.2242(9.525  draught  between  back  and 
3138894  front  rollers. 


1833480 
1743830 


896500 
697532 


1989680 
1743830 


245850  • 

The  draught  in  rollers  at  mules  is  required  from  the  following 
particulars: — 

Wheel  on  front  rollers  24  teeth,  working  into  wheel  100  teeth  on 
shaft  for  driving  back  rollers  ;  change  wheel  25  teeth  on  same 
shaft,  works  into  wheel  50  teeth  on  back  rollers. 

Diameter  of  back  rollers,  |  inch. 

Diameter  of  front  rollers,  1  inch. 

DRIVING-WHEELS. 

24  teeth  wheel  on  front  roller. 

25  teeth  wheel,  or  change  pinion. 


120 
48 


600 

.875,  or  I  inch  diameter  of  back  rollers. 


525.000  divisor. 

DRIVEN-WHEELS. 

100  teeth  wheel  on  shaft  for  driving  back  rollers. 
50  teeth  wheel  on  do. 


5000 

1  inch  diameter  of  front  rollers. 


6000  dividend. 


1 


MULES. 


151 


525)5000(9.521  draught  between  back  and  front 
4725  rollers. 


2750 
2625 


1250 
1050 


2000 

2100— nearly. 

iV,  B. — The  small  difference  between  this  and  the  last  example, 
arises  from  the  decimal  fractions,  ivhich  occur  in  the  other  sys- 
tem of  ivorlcing. 

If  the  front  rollers  deliver  55  inches  each  stretch,  which  puts 
up  60  inches;  the  gain  or  draught  in  the  carriage  will  be  5  inches, 
which  is  equal  to  lyS  draught;  the  draught  in  the  rollers  is 
9.524  ;  what  will  the  total  draught  be  ? 

9.524  draught  in  rollers. 

60  inches  length  of  stretch. 


r  5)571.440 

Delivd.  from  rols.  55  in.  <  

(11)114.288 

  ^ 

10.3899,  or  10/a  (nearly),  total 
draught  at  mules. 

If  the  total  draught  at  mules  be  10.39,  and  the  numbers  to  be 
spun  40's ;  the  length  required  to  be  spun  20  hanks  a  spindle  a 
week,  the  number  of  spindles  in  the  mules  1000;  what  hank 
roving  will  be  required,  what  number  of  hanks,  and  what  weight? 

RULE. 

Multiply  the  number  of  spindles  in  the  mules,  by  the  number 
of  hanks  required  a  spindle,  and  the  product  will  be  the  total 
number  of  hanks  of  yarn  produced  a  week ;  which,  divided  by 
the  draught,  will  give  the  number  of  hanks  of  roving  required. 
Then  divide  the  numbers  of  yarn  by  the  draught  in  the  mules, 
and  the  quotient  will  be  the  hank  roving.    Then  divide  the 


152 


MULES. 


number  of  hanks  of  roving  required  to  produce  the  given  length 
of  yarn,  by  the  hank  roving,  and  the  quotient  will  be  the  weight 
of  roving  required. 


EXAMPLE. 


1000  number  of  spindles  in  mules. 

20  hanks,  length  required  a  spindle. 


20000  total  number  of  hanks. 
Hanks. 

Draught  10.39)20000(1925  nearly,  hanks  of  roving  required. 
1039 


9610 
9351 


2590 
2078 

5120 

6195 — nearly. 

Nos.  of  yarn. 
Draught  10.39)40.00(3.85  hank  roving  required. 
3117 


8830 
8312 

5180 

5195 — nearly. 
Hanks. 

Hank  roving,  3.85)1 925(500ibs.  net  weight  of  roving  required. 
1925 

The  speed  of  the  scroll  is  required  from  the  following  par- 
ticulars:— 

Revolutions  of  rim-shaft  a  minute,  270.74. 

Wheel  on  rim-shaft  20  teeth,  working  into  wheel  60  teeth  on 

short  driving-shaft. 
Wheel  on  bottom  end  of  short  driving-shaft,  32  teeth,  working 

into  wheel  100  teeth  on  scroll-shaft. 


MULES. 


153 


270.74  revolutions  of  rlm-shaft  a  min. 
20  teeth  wheel  on  rim-shaft. 


5414.80 

32  teeth  wheel  on  bottom  end  of  short 

  driver. 

108296 
162444 


173273.6  dividend. 

60  teeth  wheel  on  top  of  short  driver. 
100  teeth  wheel  on  scroll-shaft. 


6000  divisor. 
6.000)173.273.6 


28.879  nearly,  revols.  of  scroll-shaft  a  min. 

If  the  scroll  makes  28.879  revolutions  a  minute,  and  be  4 
inches  diameter  ;  what  will  it  traverse  ? 

28.879  revolutions  of  scroll  a  minute. 
4  inches,  diameter  of  scroll. 


115.516 

3.1416  circumference  when  diameter  is  1. 


693096 
115516 
462064 
115516 
346548 


362.9050656  nearly  363  inches,  scroll  trav.  a  min. 

The  gain,  or  draught  in  carriage  is  required  from  the  follow- 
ing particulars : — 

Scroll  traverses  a  minute,  362.9050656  inches. 
Front  rollers  traverse  a  minute,  332.2242  inches. 
11 


154 


MULES. 


332.2242)362.9050656(1.09235  gain,  or  draught  in 
3322242  carriage. 


30680865 
29900178 


7806876 
6644484 


11623920 
9966726 


16571940 
16611210— nearly. 

By  multiplying  the  draught  in  rollers,  by  the  draught,  or  gain 
in  carriage,  it  will  give  the  total  draught  at  mules. 

If  the  length  of  the  stretch  be  61  inches,  and  the  gain  or 
draught  in  carriage  be  1.09235,  what  length  will  the  rollers 
deliver,  and  how  many  inches  will  the  carriage  gain  a  stretch? 

Inches  stretch. 

Draught  at  carriage,  1.09235)61.00000(55.8429  inches,  delivered 

546175  at  rollers  a  minute. 


638250 
546175 


920750 
873880 


468700 
436940 


317600 
218470 


991300 
983115 


8185 


MULES, 


155 


61.0000  inches,  length  of  stretch. 
55.8429  inches,  delivered  at  rollers. 


5.1571  inches,  carriage  gains. 

The  speed  of  the  spindles  at  mules  is  required  from  the  fol' 
lowing  particulars  : — 

Revolutions  of  rim-shaft  a  minute,  270.74. 
Diameter  of  rim,  23j  inches. 
Diameter  of  rim-band-pulley,  18J  inches. 
Diameter  of  twist-pulley,  14J  inches. 
Diameter  of  drums  in  carriage,  10  inches. 
Diameter  of  wharves,  J  inch. 

270.74  revolutions  of  rim  a  minute. 
23.25  inches,  diameter  of  rim. 


135370 
54148 
81222 
54148 


6294.7050 

14.25  inches,  diameter  of  twist-pulley. 


31473525 
12589410 
25178820 
6294705 


89699.54625  dividend. 

18.25  inches,  diameter  of  rim-band-pulley. 
.75,  or  f  inch,  diameter  of  wharves. 


9125 
12775 


13.6875  divisor. 


156 


MULES. 


13.687)89699.54625(65.536  revolutions  of  spindles 
82122  at  mules  a  minute. 


75775 
68435 


73404 
68435 


49696 
41061 


86352 
82122 


4230 

If  the  scroll  at  a  pair  of  mules  traverse  at  the  rate  of  363 
inches  a  minute,  and  the  spindles  make  6553  revolutions ;  how 
many  turns  an  inch  will  there  be  in  the  yarn  ? 

363)6553(18.05  turns  an  inch  in  yarn,  while  carriage  is 
363  coming  out. 

2923 
2904 


1900 
1815 


85 

How  many  turns  will  the  rim  make  a  stretch,  if  the  front 
rollers  deliver  57  inches,  allowing  the  rim  to  make  271  revolu- 
tions, while  the  front  rollers  deliver  332.224  inches? 

RULE. — Multiply  the  revolutions  of  the  rim  by  the  length  of 
the  stretch,  and  divide  by  the  number  of  inches  delivered  at 
the  front  rollers,  and  the  quotient  will  be  the  revolutions,  or 
turns  of  rim  a  stretch. 


MULES. 


157 


271  revolutions  of  rim. 
57  inches  length  of  stretch. 


1897 
1355 


Inches  delivered,  332.224)15447.000(46.4957  revolutions,  or 

1328896  turns  of  rim  a 
 stretch. 

2158040 

1993344 


1646960 
1328896 


3180640 
2990016 


1906240 
1661120 


2451200 
2325568 


125632 

To  find  the  number  of  turns  required  for  twist,  or  weft  an  inch.  \ 
RULE. — For  twist,  multiply  the  square  root  of  the  numbers,  or 
counts  of  yarn  by  3.75,  or  3f,  and  for  weft,  multiply  the 
square  root  of  the  numbers,  or  counts  of  yarn  by  3.25,  or  3J, 
and  the  products  will  be  the  turns  an  inch  required. 

What  number  of  turns  an  inch  will  44's  twist  require,  accord- 
ing to  the  foregoing  rule  ? 

COUNTS. 

44(6.633  square  root  of  44. 
36 


126)800 
756 


1323)4400 

3969  39789 


13263)43100  3311 


158 


MULES. 


6.633  square  root  of  44. 
3.75,  or  3|. 


33165 
46431 
19899 


24.87375,  or  nearly  25  turns  an  inch,  required  for 

No.  44's  twist. 

What  number  of  turns  an  inch  will  36's  weft  require? 
6  is  the  square  root  of  36. 
3.25 


19.50,  or  19J  turns  an  inch  required  for  36's  weft. 

What  number  of  turns  an  inch  will  lOO's  twist  require? 
10  is  the  square  root  of  100. 
3.75 


37.50,  or  37f  turns  an  inch  required  for  No.  lOO's 

twist. 

The  preceding  rules  for  ascertaining  the  turns  an  inch  required 
for  twist  and  weft,  have  been  generally  adopted ;  however,  where 
a  good,  or  even  a  fair  quality  of  cotton  is  used,  the  following 
rule  will  be  found  to  answer,  particularly  for  some  qualities  of 
yarns. 

RULE. — Multiply  the  numbers,  or  counts  of  yam  by  12,  the 
square  root  of  which  gives  the  turns  an  inch  required  for  twist. 
Weft  will  require  3J,  or  4  turns  an  inch  less  than  twist. 

N.  B. — Some  cotton  requires  more  twist  than  others,  according 
to  its  quality. 

What  number  of  turns  an  inch  will  be  required  for  No.  50's 
twist,  or  weft,  according  to  the  above  rule? 

50's  numbers,  or  counts  of  yarn. 
12 


600(25  turns  nearly,  required  for  50's  twist,  less 
4  3J  turns  for  weft. 


45)200 

225 — nearly. 


MULES.  \<-  7^59 

What  number  of  turns  an  incli  ■will  be  required  for  lOO's  twist'," 
or  weft? 

lOO's  numbers,  or  counts  of  yarn. 
12 


1200(34.64  turns  an  inch  required  for  No.  lOO's 
9  twist,  less  3J  turns,  which  will  be  equal 

  to  31.14  turns  an  inch  for  lOO's  weft. 

64)300 
256 


686)4400 
4116 


6924)28400 
27696 


704 

RULE  for  ascertaining  the  revolutions  of  spindles,  for  the  rim 
1. — Multiply  the  diameters  of  the  driving-pulleys  together  for 
a  dividend,  and  the  driven-pulleys  accordingly  for  a  divisor, 
and  the  quotient  will  be  the  revolutions  of  the  spindles  for  the 
rim  1. 

If  the  rim  and  rim-band-pulleys  be  each  22  inches  diameter, 
the  twist  pulley  13J  inches,  and  the  wharves  |  inch ;  what  revo- 
lutions or  turns  will  the  spindles  make  for  the  rim  1? 

N.  B. —  The  rim  and  rim-band-pulley  being  of  the  same  diameters 
are  omitted  in  the  working. 

Diameter  of  wharves,  .875)13.500(15.428  revolutions  of  spindles 

875  for  rim  1. 


4750 
4375 


3750 
3500 


2500 
1750 


7500 
7000 


500 


160 


MULES. 


If  the  rim  be  33  inches  diameter,  the  rim-band-pulley  26 
inches,  the  twist-pulley  14J  inches,  and  the  wharves  f  of  an 
inch ;  what  number  of  revolutions,  or  turns  will  the  spindles 
make  for  the  rim  1? 

DRIVERS. 

Twist-pulley,  14.25  inches. 
Rim,      33  inches. 

4275 
4275 


470.25  dividend. 

DRIVEN. 

26  inches  drum-band-pulley. 
.75,  or  I  inch  wharves. 

130 
182 


19.50  divisor. 

195.)470.25(24.115  revols.  of  spindles  for  rim  1. 
390 


802 
780 


225 
195 


300 
195 


1050 
975 


75 


BELL-WHEEL,  OR  REVOLUTIONS  OP  RIM  A  STRETCH. 

EXILE. — Multiply  the  turns  required  an  inch,  by  the  number  of 
inches  in  the  length  of  the  stretch,  for  a  dividend,  and  divide 


1 


MULES. 


161 


by  the  revolutions,  or  turns  the  spindles  make  for  the  rim  1, 
and  the  quotient  will  be  the  number  of  teeth  for  the  bell-wheel, 
or  revolutions  of  rim  a  stretch. 

If  18.62  turns  an  inch  be  required,  and  the  length  of  the 
stretch  be  58  inches,  the  revolutions  or  turns  of  spindles  15.428 
for  the  rim  1 ;  what  number  of  teeth  must  there  be  in  the  bell- 
wheel,  or  what  revolutions  must  the  rim  make  a  stretch? 

18.62  turns  required  ah  inch. 
58  inches,  length  of  stretch. 


14896 
9310 


15.428)1079.96(70  teeth  required  for  bell-wheel,  or  re- 
107996      volutions  of  rim  a  stretch. 

The  turns  an  inch  are  required  from  the  following  particulars : — 
Bell- wheel,  70  teeth;  rim,  22  inches  diameter;  rim-band-pulley, 
22  inches  diameter;  twist-pulley,  13J  inches  diameter;  drums 
in  carriage,  10  inches  diameter;  wharves,  ^,  or  .875  inch 
diameter,  and  length  of  stretch,  58  inches. 

N.B. — The  rim,  rim-hand,  pulley,  and  drum  in  carriage  are 
omitted,  on  account  of  being  drivers  and  driven  of  the  same 
dimensions. 

Multiply  the  number  of  teeth  in  the  bell-wheel,  by  the  diame- 
ters of  the  driving-pulleys  respectively  for  a  dividend;  then 
multiply  the  number  of  inches  in  the  length  of  a  stretch,  by  the 
diameters  of  the  driven-pulleys  accordingly  for  a  divisor,  and  the 
quotient  will  be  the  revolutions  or  turns  an  inch. 

58  inches,  length  of  stretch. 
.875,  or  I  inch,  diameter  of  wharves. 


7000 
4375 


50.750  divisor. 

13.5  or  13J  inches,  diameter  of  twist-pulley. 
70  teeth  bell-wheel,  or  re  vols,  of  rim  a  stretch. 


94.5000 


162 


MULES. 


50.75)94.5000(18.62  turns  an  inch. 
5075 


43750 
40600 


31500 
30450 


10500 
10150 


350 

If  26  turns  an  inch  be  required,  and  the  length  of  the  stretch 
be  61  inches;  the  revolutions,  or  turns  of  the  spindles  24.115  for 
the  rim  1 ;  what  number  of  teeth  must  there  be  in  the  bell-wheel, 
or  what  revolutions  must  the  rim  make  a  stretch  ? 

26  turns  an  inch. 

61  inches,  length  of  stretch. 

26 
156 


24.115)1586.000(65.768,  or  nearly  66  teeth  required 
144690  for  bell-wheel,  or  revolu- 
 tions  of  rim  a  stretch. 

139100 

120575 


185250 
168805 


164450 
144690 


197600 
192920 


4680 

The  turns  an  inch  are  required  from  the  following  particulars : — 
Bell-wheel,  66  teeth;  length  of  stretch,  60  inches;  diameter  of 
rim,  33  inches;  diameter  of  rim-band-pulley,  26  inches;  diame- 
ter of  twist-pulley,  14 J  inches;  diameter  of  drums  in  carriage, 
10  inches,  and  diameter  of  wharves,  |  inch. 


MULES. 


163 


66  teeth  bell-wheel. 

33  inches,  diameter  of  rim. 


198 
198 


2178 

14.25,  or  14J  inches,  diameter  of  twist-pulley. 


10890 
4356 
8712 
2178 


31036.50  dividend. 

26  inches,  diameter  of  twist-pulley. 
60  inches,  length  of  stretch. 


1560 

.75,  or  f  inch,  diameter  of  wharves. 


7800 
10920 


1170.00  divisor. 

1170.)31036.5(26.52  turns  an  inch  required. 
2340 


7636 
7020 


6165 
5850 


3150 
2340 


810 

Whatever  the  principle  of  the  mules  is,  any  particular  may  be 
found  by  attending  to  the  rules  and  examples  illustrated. 
iV!  B. —  The  general  rules  are  exemplified  tvith  the  different  tables, 

and  will  appear  in  their  regular  course. 


164 


TABLES. 


TABLES, 


Showing  the  size,  hank,  and  j^roportion  of  hank  in  every  ope- 
ration, from  the  lap  machine  through  all  the  various  processes  of 
carding,  drawing,  slabbing,  roving  and  spinning,  with  practical 
rules  and  examples. 


EXPLANATION  OF  THE  CARDING  AND  DRAWING-TABLES. 

The  first  line  in  the  carding  and  drawing-table  is  the  decimal 
of  the  hank  according  to  its  length  and  weight,  which  will  be 
found  in  the  following  manner:  Multiply  all  the  draughts  to- 
gether as  far  as  regards  the  operation  you  intend  trying,  whether 
it  be  slabbing,  drawing,  or  carding,  for  a  dividend,  and  all  the 
doubling  accordingly  for  a  divisor,  the  quotient  will  be  the 
draught ;  then  divide  the  numbers  you  are  spinning,  or  the  num- 
bers you  wish  to  spin,  by  the  net  draught,  and  the  quotient  will 
be  the  decimal  of  the  hank ;  opposite  to  which  in  the  table,  you 
will  have  the  weight  according  to  the  length  weighed. 


Suppose  the  total  draught  to  be  181440,  the  doubling  1728, 
and  the  numbers  to  be  spun  40's ;  what  weight  will  2  yards  of 
carding,  or  doubling  be  ? 

1728)181440(105  draught  more  than  doubling. 
1728 


EXAMPLE. 


8640 
8640 


Draught  more  than 
doubling. 


Counts. 
105)40.0(0.38 
315 


decimal  of  a  hank.  Opposite 
to  which  in  the  table  under 
2  yards  will  be  found,  1  dwt. 
19.8  grains,  the  weight  re- 
quired. 


850 
840 


10 


CARDING  AND  DRAWING-TABLE. 


165 


CARDING  AND  DRAWING-TABLE. 


From  .05  to  .089  decimal  of  hank  for  2,  4,  and  6  yards. 


Dec.  of 

2  yards. 

Dec.  of 
hank. 

4  yards. 

Dec.  of 

6  yards. 

hank. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

nank. 

oz. 

dwts. 

grains. 

n^i 
.uo 

1  Q 

91  QQ 

Of; 

Q 

y 

1  Q  1  R 

0*1 

9 

0 

e 

0. 

1  o 

1  /<  7Q 

O^i  1 

Q 

y 

O  OR 

O^i  1 

9 
4 

4 

y.oo 

1  Q 
1  o 

o.0 1 

0fi9 

Q 

1  1  fi9 

01^9 

.  v04 

9 
4 

o 
o 

14. Oo 

9  4R 

0^1 'I 

7 

7 

9Q  4Q 

.uoo 

/it 

4 

on  QO 
4U.oy 

1  9 

9n  A^i 

7 

1  1  7S 

.U04 

9 

4 

o  no 

4.y4 

1  9 

1  ^  HQ 
i  O.Uo 

O'l'S 

.U 

7 

7 

0  (iR 
U.OO 

0*1 
.UOO 

9 

1 
1 

1  C\  f\C\ 

1  u.uy 

1  9 

Q  R  1 
y.D  1 

OPiR 

O 

1  Q  7Q 
lo.  I  o 

.uoo 

9 

n 
U 

1 7.O0 

.Vt)  / 

1  9 

zl  QO 

i.oy 

nfi7 
.uo  / 

ft 
D 

Q  9Q 

0^17 

.U.J  / 

9 

A 

U 

O   1  Q  1 
4.  lo 

1  1 
1  1 

5 

17  91 

.uoo 

1 
1 

1  7 
1  / 

lo.oo 

1  1 
i  i 

1  o.'lo 

O^iQ 

5 

7  47 

.uoo 

1 

1 

17 
17 

1  .yo 

OR 

1  1 
1  X 

1  Q  77 

OR 

4 

99  Ofi 
.44.U0 

OR 

1 

1  0 

1 1  .oo 

.UOl 

1  1 
1  1 

Q  99 

0R1 

4 

1  9  Q4 

ORI 

.U  U  1 

1 

1 

1 0 

oo  1  ^ 
44.17 

1  1 
1  1 

A  fH 
•l.O  1 

0fi9 

4 

4  1  Q 
4.10 

0R9 

.UU4 

1 

1 

1  0 

o.yo 

1  1 

J.  1 

0 

u.oo 

OR^ 

3 

1  Q  R 
ly.D 

ORQ 
.uuo 

1 
1 

1  A 
1 4 

OA   1  ^ 
4U.  10 

1  1 

90  A  1 

0R4. 

3 

1  1 

1  1  .00 

0R4 

1 

1  A 
1 4 

7  .ii 

1  0 
1  U 

1  R  /I  1 

ORIS 

3 

Q  Q9 
o.o^ 

OR'i 
.uuo 

1 
1 

1  o 

iy.7o 

.UuD 

1  0 

1  9  1^9 

ORR 

2 

1  Q  ^ 

ly.oo 

ORR 
.uuo 

1 
1 

1  Q 
1  o 

O.U7 

nfi7 

1  u 

ft  7 

0R7 

2 

19  01 
14. Ul 

0fi7 

1 
1 

1  9 
1 4 

40. 7o 

1  0 
1  u 

OQ 

ORR 

2 

4  RQ 

ORR 

1 
1 

1  9 
14 

Q  "^Q 

y.7y 

nfiQ 
.uuy 

1  .'10 

ORQ 

1 

91  41 

ORQ 
.uuy 

1 
1 

1  1 

O.)  Q>'Y 
44. o7 

.U  i 

Q 

99  OQ 

07 

I 

1  4  RQ 
1 4.  oy 

07 
.u  / 

1 

1  1 

1  O 

1  4.0 

.U  /  1 

Q 

y 

1  Q  7/1 
lo.  /'I 

07  1 

1 

7  Oft 

071 
.U  /  1 

1 

1 

1 1 

O  I'^'O 
4.74 

079 

Q 

y 

1  o.oy 

079 

V  1 

9  9Q 

079 
.U  <  4" 

1 

1 

lU 

1  Q  1  Q 

lo.iy 

f»7^ 
.U  /  o 

Q 

y 

1  9  Q  1 

07^ 

0 

1  Q  1  9 

iy.i4 

07  Q 
.U  /  o 

1 

1 

<y  AO 

074 

Q 

y 

Q  9.'> 

074 

0 

1  9  Qf^ 

14. yo 

074 

1 

1 

Q 

y 

oo  1  ^ 
44.17 

07^ 

9 

6.22 

07f^ 

0 

6.94 

07^1 

.u  /  o 

1 

1 

9 

13.21 

9 

3.29 

07  R 

0 

l.l 

07R 
.u  /  o 

1 

1 

9 

4.39 

.077 

9 

0.45 

.077 

18 

0.9 

.077 

1 

8 

19.85 

.078 

8 

21.67 

.078 

17 

19.35 

.078 

1 

8 

11.52 

.079 

8 

18.97 

.079 

17 

13.94 

.079 

1 

8 

3.41 

.08 

8 

16.33 

.08 

17 

8.66 

.08 

1 

7 

19.5 

.081 

8 

13.76 

.081 

17 

3.52 

.081 

1 

7 

11.78 

.082 

8 

11.25 

.083 

16 

22.5 

.082 

1 

7 

4.25 

.083 

8 

8.8 

.083 

16 

17.6 

.083 

1 

6 

20.9 

.084 

8 

6.41 

.084 

16 

12.82 

.084 

1 

6 

13.37 

.085 

8 

4.07 

.085 

16 

8.15 

.085 

1 

6 

6.73 

.086 

8 

1.79 

.086 

16 

3.59 

.086 

1 

5 

23.89 

.087 

7 

23.57 

.087 

15 

23.14 

.087 

1 

5 

17.21 

.088 

7 

21.39 

.088 

15 

18.78 

.088 

1 

5 

10.68 

.089 

7 

19.26 

.089 

15 

14.53 

.089 

1 

5 

4.29 

166  EXAMPLES. 

What  will  8  yards  of  .08,  or  ^     hank  weigh  ? 
Proportion  of  hank,  .08)66.66 

No.  of  grains  in  1  oz.,  437.5)833.33  grains,(l  oz. 

437.5 


1  (Iwt.  is  24  grains,)395.83(16  dwts. 
24 


155 
144 


11.83  grains. 

Weight  of  8  yards  of  .08  decimal  of  hank  drawing,  will  be  1 
oz.,  16  dwts.,  11.83  grains. 

If  8  yards  of  drawing  weigh  1  oz.,  16  dwts.,  11.83  grains, 
what  size  or  proportion  of  hank  will  it  be  ? 

1  ounce  437.5  grains. 

16  dwts.  X  24  grains  384.  grains. 

11.833  grains. 


1  oz.,  16  dwts.,  11.83  grains,  833.333 
The  dividend  for  8  yards  is  Q6.66d. 

833. 33)66. 6666(.08  decimal  of  a  hank,  or  size  of 
666066  drawing. 

What  will  6  yards  of  .1,  or  Jq  hank  drawing  weigh  ? 

Dividend  for  6  yards  is  50.    (See  Table  of  Dividends.) 
0.1 j50. 


500  grains  weight. 
1  ounce,437.5  grains, )500. 0(1  oz. 

437.5 


1  dwt.  is  24  grains,)62.5(2  dwts. 

48 


14.5  grains. 

Weight  of  6  yards  of  0.1,  or  j'g  hank  drawing,  will  weigh  1 
oz.,  2  dwts.,  14:1  grains. 


CARDING  AND  DRAWING-TABLE.  "■r5-/^7    "  ''^'7\j 

CARDING  AND  DRAWING-TABLE. 


From  .09  to  .129  decimal  of  hank  for  2,  4,  and  6  yards. 


Dec.  of 

2  yards. 

Dec.  of 

4  yards. 

Dec.  of 

6  yards. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

.09 

7 

17  18 

.09 

Il\J  tO  4 

.09 

1 
1 

A 
+ 

99  (\^ 

.091 

7 

15.15 

.091 

15 

6  ^ 

.091 

1 

X 

A. 

1  0,\30 

.092 

7 

13.15 

.092 

15 

2.3 1 

.092 

\ 

A 

.093 

7 

1 1.21 

.093 

14 

22.42 

.093 

I 

4 

.094 

7 

4 

9.3 

.094 

14 

18.6 

.094 

I 

Q 
o 

99  41 

.095 

7 

7  43 

.095 

14 

14.87 

.095 

I 

o 

1  n  1 

.096 

7 

5.61 

.096 

14 

1 1 .22 

.096 

I 

o 

1  1  .oo 

.097 

7 

3.82 

.097 

14 

7  64 

.097 

I 

Q 
t> 

.098 

7 

2.06 

.098 

14 

d  1  "i 

.098 

I 

Q 
o 

0  7 

.099 

7 

0.35 

.099 

14 

0  7 

.099 

J 

9 

.1 

Q 

22.66 

1 

13 

21 

.1 

9 

.101 

5 

21.01 

.101 

13 

1  H  0^ 

X  O  .  V/ .  J 

.101 

1 

9 

Q  0^ 

.102 

g 

19.39 

.102 

13 

]  4,79 

.102 

I 

9 

.103 

g 

17.81 

.103 

13 

1 1 .62 

.103 

I 

9^ 

.104 

6 

16.25 

.104 

13 

O .  1 

.104 

I 

1  Q  9fi 

.105 

g 

14.72 

.105 

13 

5.46 

.105 

I 

1  ^.  uo 

.106 

g 

13.13 

.106 

13 

2.27 

.106 

I 

£7 .  i/  1 

.107 

g 

1 1.76 

.107 

12 

.107 

1 

X 

^  7ft 

.108 

g 

10.32 

.108 

12 

20.64 

.108 

J 

1  .tu 

.109 

g 

8.9 

.109 

12 

17  81 

.109 

1 

X 

0 
u 

91  9  1 

.11 

g 

7.51 

.11 

12 

1  f)^ 
1.  o^yjo 

.11 

1 

X 

0 
u 

1  7  04 

.111 

g 

6.15 

.111 

12 

19^ 

.111 

1 

0 

.112 

g 

4.98 

.112 

12 

Q  97 

.112 

1 

X 

n 

.113 

g 

3.49 

.113 

12 

6.98 

.113 

1 

X 

0 

4  Q7 

.114 

g 

2.19 

.114 

12 

.114 

1 

X 

0 

1  HQ 

.115 

6 

0.92 

.115 

12 

1.85 

.115 

18 

2.78 

.116 

5 

23.67 

.116 

11 

23.35 

.116 

17 

23.03 

.117 

5 

22.45 

.117 

11 

20.9 

.117 

17 

19.35 

.118 

5 

21.24 

.118 

11 

18.48 

.118 

17 

15.72 

.119 

5 

20.05 

.119 

11 

16.11 

.119 

17 

12.16 

.12 

5 

18.88 

.12 

11 

13.77 

.12 

17 

8.66 

.121 

5 

17.74 

.121 

11 

11.48 

.121 

17 

5.22 

.122 

5 

16.61 

.122 

11 

9.22 

.122 

17 

1.83 

.123 

5 

15.5 

.123 

11 

7. 

.123 

16 

22.5 

.124 

5 

14.4 

.124 

11 

4.81 

.124 

16 

19.22 

.125 

5 

13.33 

.125 

11 

2.66 

.125 

16 

16. 

.126 

5 

12.27 

.126 

11 

0.5 

.126 

16 

12.82 

.127 

5 

11.23 

.127 

10 

22.46 

.127 

16 

9.7 

.128 

5 

10.2 

.128 

10 

20.41 

.128 

16 

6.62 

.129 

5 

9.19 

.129 

10 

18.39 

129 

16 

3.59 

168 


EXAMPLES. 


The  follo'win";  will  be  the  dividends,  according  to  the  number 
of  yards  for  ascertaining  the  weight  of  any  decimal  part  of  a 
hank. 


Yards 

T)i  viflpnf^c! 

1 

8.333 

2 

16.6Q6 

3 

25. 

4 

33  333 

5 

41.666 

6 

60. 

7 

58!333 

8 

66.666 

9 

■  75. 

10 

83.333 

15 

125. 

20 

166. 

30 

250. 

40 

333.333 

60 

500. 

80 

666.666 

120 

1000. 

RULE. — Divide  the  dividend  by  the  hank,  or  decimal  part  of  a 
hank,  according  to  the  number  of  yards  weighed,  and  the  quo- 
tient will  be  the  weight  in  grains. 

What  will  2  yards  of  0.13  of  a  hank  weigh? 

Dividend  for  2  yards. 
13)16.666(128.2  grains,  or  5  dwts.,  8.2  grains, 
13  weight  of  2  yards. 


36 
26 


106 
104 


26 
26 


CARDING  AND  DRAWING-TABLE. 


169 


CARDING  AND  DRAWING-TABLE. 


From  .13  to  .187  decimal  of  hank  for  2,  4,  and  6  yards. 


1 

1  Dec.  of 
1  hank. 

2  yards. 

Dec.  of 
hank. 

4  yards. 

Dec.  of 
hank. 

6  yards. 

dvvts. 

grains. 

oz. 

dvvts. 

grains. 

oz. 
— 

dvvts. 

grains. 

1 

j  .13 

5 

8.2 

.13 

10 

16.4 

.13 

16 

0.6 

.131 

5 

7.22 

.131 

10 

14.45 

.131 

15 

21.67 

.132 

5 

6.26 

.132 

10 

12.5 

.132 

15 

18.78 

.133 

5 

5.31 

.133 

10 

10.62 

.133 

15 

15.93 

.134 

5 

4.37 

.134 

10 

8.75 

.134 

15 

13.13 

.135 

5 

3.45 

.135 

10 

6.91 

.135 

15 

10.37 

.136 

5 

2.55 

.136 

10 

5.2 

.136 

15 

7.74 

.137 

5 

1.65 

.137 

10 

3.3 

.137 

15 

4.96 

.138 

5 

0.77 

.138 

10 

1.54 

.138 

15 

2.31 

.139 

4 

23.9 

.139 

9 

23.8 

.139 

14 

23.7 

.14 

4 

23. 

.14 

9 

22. 

.14 

14 

21. 

.141 

4 

22.2 

.141 

9 

20.4 

.141 

14 

18.6 

.142 

4 

21.37 

.142 

9 

18.74 

.142 

14 

16.1 1 

.143 

4 

20.55 

.143 

9 

17.1 

.143 

14 

13.65 

.144 

4 

19.74 

.144 

9 

15.48 

.144 

14 

1 1 .22 

.145 

4 

12.94 

.145 

9 

13.88 

.145 

14 

8.82 

.146 

4 

18.15 

.146 

9 

12.31 

.146 

14 

6.46 

.147 

4 

17.37 

.147 

9 

10.75 

.147 

14 

4.13 

.148 

4 

16.61 

.148 

9 

9.22 

.148 

14 

1.83 

.149 

4 

15.85 

.149 

9 

7.71 

.149 

13 

23.57 

.15 

4 

15. 11 

.15 

9 

6.22 

.15 

13 

21.33 

.151 

4 

14.37 

.151 

9 

4.75 

.151 

13 

19.12 

.1525 

4 

13.29 

.1525 

9 

2.57 

.1525 

13 

15.86 

.153 

4 

12.93 

.153 

9 

1.86 

.153 

13 

14.79 

.155 

4 

11.52 

.155 

8 

23.05 

.155 

13 

10.58 

.157 

4 

10.15 

.157 

8 

20.31 

.157 

13 

6.47 

.1575 

4 

9.82 

.1575 

a 

o 

1 9.6 

.1575 

13 

5.46 

.159 

4 

8.82 

.159 

8 

17.64 

.159 

13 

2.46 

.16 

4 

,  8.16 

.16 

8 

16.33 

.16 

13 

0.5 

.163 

4 

6.24 

.163 

8 

12.49 

.163 

12 

18.74 

.165 

4 

5.1 

.165 

8 

10.2 

.165 

12 

15.3 

.167 

4 

3.8 

.167 

8 

7.6 

.167 

12 

11.4 

.17 

4 

2. 

.17 

8 

4. 

.17 

12 

6. 

.173 

4 

0.33 

.173 

8 

0.67 

.173 

12 

1.01 

.175 

3 

23.32 

.175 

7 

22.65 

.175 

11 

21.98 

.179 

3 

21.1 

.179 

7 

18.21 

.179  I 

1 1 

15.3-2 

.18 

3 

20.59 

.18 

7 

17.18 

.18 

1 1 

13.77 

.183 

3 

19.07 

.183 

7 

14.14 

.183 

11 

9.22 

.185 

3 

18.1 

.185 

7 

12.18 

.185 

1 1 

6.27 

.187 

3 

"■'1 

.187 

7 

10.25 

.187 

I  11 

3.37 

12 


170  EXAMPLES. 

What  will  4  yards  of  0.26  of  a  hank  weigh? 

0.26)33.333(128.2  grains,  or  5  dwts.,  8.2  grains. 
26 


73 

52 


213 
208 


53 
52 


1 

What  will  6  yards  of  0.335  of  a  hank  weigh? 

0.335)50.000(149.25  grains,  or  6  dwts.  5i  grains. 
335 


1650 
1340 


3100 
3015 


850 
670 


1800 
1675 


125 

If  6  yards  of  carding,  or  drawing  weigh  6  dwts.,  5j  grains, 
what  will  the  decimal  of  the  hank  be? 

6  dwts.  51  grs.  =  149.25  grs.)50.0000(0.335  decimal  of  a  hank, 

44775        and  opposite  which  in 

■   the  table  under  6  yards 

52250  will  be  found  6  dwts. 
44775       51  grains. 


74750 
74625 


125 


CARDING  AND  DRAWING-TABLE. 


171 


CARDING  AND  DRAWING-TABLE. 


From  .19  to  .31  decimal  of  hank  for  2,  4,  and  6  yards. 


Dec.  of 

2  yards. 

Dec.  of 
hank. 

4  yards. 

Dfic.  of 
hank. 

6  yards. 

dwts. 

grains. 

oz 

dwts. 

grams. 

oz 

dwts. 

grams. 

.19 

Q 

15.71 

.19 

7 

4 

7.43 

.19 

10 

23.15 

.193 

3 

14.35 

.193 

7 

4.71 

.193 

10 

19.06 

,195 

Q 
o 

13.47 

.195 

7 
* 

2.94 

.195 

10 

16.41 

.197 

3 

12,6 

.197 

7 

1.2 

.197 

10 

13.8 

.2 

3 

1 1.33 

.2 

6 

22.66 

.2 

10 

10. 

.203 

3 

10.09 

.203 

Q 

20.2 

.203 

10 

6.3 

.205 

3 

9.3 

.205 

Q 

18.6 

.205 

10 

3.9 

.207 

3 

8.51 

.207 

Q 

17.03 

.207 

10 

1.54 

.21 

3 

7.36 

.21 

g 

14.73 

.21 

9 

22.1 

.213 

3 

6.24 

.213 

Q 

12.49 

.213 

9 

]  8.74 

.215 

3 

5.51 

.215 

Q 

1 1.03 

.215 

9 

16.55 

.217 

3 

4.8 

.217 

6 

9.6 

.217 

9 

14.4 1 

.22 

3 

3.75 

.22 

6 

7.51 

.22 

9 

1 1.27 

.223 

3 

2.73 

.223 

6 

5.46 

.223 

9 

8.21 

.225 

3 

2.07 

.225 

5 

4.14 

.225 

9 

6.22 

.227 

3 

1.42 

.227 

6 

2.84 

.227 

9 

4.26 

.23 

3 

0.46 

.23 

6 

0.92 

.23 

9 

1.38 

.233 

2 

23.53 

.233 

5 

23.06 

.233 

g 

22.59 

.235 

2 

22.92 

.235 

5 

21.84 

.235 

g 

20.76 

.237 

2 

22.32 

.237 

5 

20.64 

.237 

Q 

18.97 

.24 

2 

21.44 

.24 

5 

18.88 

.24 

Q 

16.33 

.243 

2 

20.58 

.243 

5 

17.17 

.243 

g 

1 3.76 

.245 

2 

20.02 

.245 

5 

16.04 

.245 

Q 

12.06 

.247 

2 

19.47 

.247 

5 

14.95 

.247 

g 

10.42 

.25 

2 

18.66 

.25 

5 

13.33 

.25 

g 

8. 

.253 

2 

17.87 

.253 

5 

11.75 

.253 

8 

5.62 

.255 

2 

17.36 

.255 

5 

10.71 

.255 

8 

4.07 

.257 

2 

16.85 

.257 

5 

9.7 

.257 

8 

2.55 

.26 

2 

16.1 

.26 

5 

8.2 

.26 

8 

0.3 

.263 

2 

15.37 

.263 

5 

6.74 

.263 

7 

22.11 

.265 

2 

14.89 

.265 

5 

5.78 

.265 

7 

20.67 

.27 

2 

13.72 

.27 

5 

3.45 

.27 

7 

17.18 

.275 

2 

12.6 

.275 

5 

1.21 

.275 

7 

13.81 

.28 

2 

11.52 

.28 

4 

23.04 

.28 

7 

10.56 

.285 

2 

10.47 

.285 

4 

20.95 

.285 

7 

7.43 

.29 

2 

9.47 

.29 

4 

18.94 

.29 

7 

4.41 

.295 

2 

8.49 

.295 

4 

16.99 

.295 

7 

1.49 

2 

7.55 

.3 

4 

15.11 

.3 

6 

22.66 

.305 

2 

6.64 

.305 

4 

13.28 

.305 

6 

19.93 

.31 

2 

5.76 

.31 

4 

11.52 

.31 

6 

17.28 

172 


EXAMPLES. 


Suppose  2  yards  of  carding,  or  drawing  weigh  2  dwts.,  20 
grains,  or  68  grains;  what  proportion  of  a  hank  will  it  be  ?  Thus 
2  yards  is      of  a  lea,  which  is  equal  to  16.666  grains,  which 
must  be  divided  by  the  weight  2  yards,  which  is  68  grains. 
2  dwts.,  20  grains,  =  68  grns.)16.666(.245  decimal,  or  proportion 

136  of  a  hank. 


306 
272 


346 
840 


6 

What  will  6  yards  of  0.4  hank  drawing  weigh  ? 
0.4)50.00 


125  grains,  or  5  dwts.,  5  grains. 

If  6  yards  of  carding,  or  drawing  weigh  5  dwts.,  5  grains ; 
what  proportion  of  a  hank  will  it  be  ? 

5  dwts.,  5  grains,  =  125  grains,)50. 000(0.4  proportion  of  hank. 

500 

What  will  3  yards  of  0.7  hank  carding,  or  drawing  weigh? 
Decimal  of  a  hank,  0.7)25.00 


1  dwt.,  is  24  grns.)35.71(l  dwt.,  11.7  grains  weight. 
24 


11.71 

What  will  4  yards  of  0.7  hank  carding,  or  drawing  weigh  ? 
Decimal  of  hank  0.7)33.333 


24)47.619(1  dwt.,  23.6  grains  weight. 
24 


23.6 


CARDING  AND  DRAWING-TABLE. 


173 


CARDING  AND  DRAWING-TABLE. 


From  .315  to  .95  decimal  of  hank  for  2,  4,  and  6  yards. 


Dec.  of 
hank. 

2  yards. 

Dec.  of 
hank. 

4  yards. 

Dec.  of 
hank. 

6  yards. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

O  1 

.o  1 0 

2 

4.91 

OIK 

.dlo 

4 

9.82 

O  "1  c 

.315 

6 

14.73 

2 

4.08 

oo 

.32 

4 

8.16 

.32 

6 

12.24 

2 

3.28 

oo  K 

4 

6.56 

.325 

6 

9.84 

.do 

2 

2.5 

o  o 
.dd 

4 

5.01 

.33 

6 

7.51 

Q  Q  f; 

.000 

2 

1.75 

O  O 
.ddO 

4 

3.5 

.335 

6 

5.25 

O  A 

2 

1. 

O  A 

.34 

4 

2. 

.34 

6 

3. 

.o40 

2 

0.3 

O  'I  K 

.345 

4 

0.61 

.345 

6 

0.92 

.do 

23.61 

O  K 

.do 

3 

23.23 

.35 

5 

22.85 

o 

22.94 

O  K  K 
.dOO 

3 

21.89 

.355 

5 

20.94 

.do 

22.29 

o  a 
.do 

3 

20.59 

.36 

5 

18.88 

O 

.dbo 

21.66 

.365 

3 

19.22 

.365 

5 

16.98 

On' 
.OI 

21.04 

.37 

3 

18.09 

.37 

5 

15.13 

.o70 

20.44 

.375 

3 

16.88 

.375 

5 

13.32 

.do 

19.86 

o  o 

.38 

3 

15.71 

.38 

5 

11.58 

.dOD 

19.29 

.385 

3 

14.58 

.385 

5 

9.87 

oo 

.dy 

18.73 

on 

3 

13.47 

.39 

5 

8.2 

OQ^ 

18.19 

OOK 

.dyo 

3 

12.38 

.390 

5 

6.58 

A 

.4 

17.66 

A 
.4 

3 

11.33 

.4 

5 

5. 

.41 

16.65 

A  1 

.41 

3 

9.3 

A  1 

.41 

5 

1.95 

A  O 

15.68 

A  O 

.44 

3 

7.36 

A  O 

4 

23.05 

/I  O 
.4d 

14.75 

A  O 
.4d 

3 

5.51 

A  O 

.43 

4 

20.28 

A  A 
.44 

13.87 

A  A 

.44 

3 

3.75 

A  A 

.44 

4 

17.63 

A  Fi 

.40 

13.03 

A 

.40 

3 

2.07 

A 

.40 

4 

15.11 

.4D 

12.23 

A  £* 

.4b 

3 

0.46 

A  a 
.4b 

4 

12.69 

A 

.4  / 

11.46 

A  ^ 

.47 

2 

22.92 

.47 

4 

10.38 

.4o 

1 

10.72 

.48 

2 

21.44 

A  O 

.48 

4 

8.16 

.4y 

10.01 

.49 

2 

20.02 

.49 

1 

.5 

9.33 

.5 

2 

18.66 

.5 

4 

4. 

.52 

8.05 

.52 

2 

16.1 

.52 

4 

0.15 

.54 

6.86 

.54 

2 

13.72 

.54 

3 

20.59 

.56 

5.76 

.56 

2 

11.52 

.56 

3 

17.28 

.58 

4.73 

.58 

2 

9.47 

.58 

3 

14.2 

.6 

3.77 

.6 

2 

7.55 

.6 

3 

11.33 

.65 

1.64 

.65 

2 

3.28 

.65 

3 

4.92 

.7 

23.8 

.7 

23.6 

.7 

2 

23.42 

.75 

22.22 

.75 

20.44 

.75 

2 

18.66 

.8 

20.83 

.8 

17.66 

.8 

2 

14.5 

.85 

19.6 

.85 

15.21 

.85 

2 

10.82 

.9 

18.51 

.9 

13.04 

•9 

2 

7.55 

.95 

17.54 

.95 

11.08 

.95 

2 

4.62 

174  EXAMPLES. 

If  8  yards  of  drawing  weigh  1  oz.,  7  dwts.,  0.5  grains;  what 
decimal  part  of  a  hank  will  it  be? 

Then  18  dwts.  5J  grains  troy  is  equal  to  1  oz.  avoirdupois; 
therefore  1  oz.,  7  dwts.,  0.5  grains  will  be  equal  to  25  dwts.,  6 
grains  troy,  or  606  grains,  which  will  be  the  divisor,  and  8  yards 
which  is      of  a  lea,  or  66.666  grains,  will  be  the  dividend. 

606  grains,)66. 666(0, 11  decimal  tof  a  hank. 
606 


606 
606 

If  10  yards  of  carding,  or  drawing  weigh  1  oz.,  12  dwts.,  18.5 
grains  ;  what  decimal  of  a  hank  will  it  be  ? 

Grains. 
1  ounce  =  437.5 
12  dwts.  =  288 
18.5 


744  grains,  in  1  oz.,  12  dwts.,  18J  grains. 

744  grains,)83.333(0.112  decimal  of  a  hank. 
744 


893 
744 


1493 
1488 


EXAMPLES.  175 

What  -will  8  yards  of  0.112  of  a  hank  drawing  weigh  ? 

Dividend. 
0.112)66.666(595.2  grains. 
560 


1066 
1008 


586 
560 

266 
224 

42 

1  oz.  is  437.5  grs.)595.2(l  oz. 

437.5 


1  dwt.  is  24  grs.)157.7(6  dwts. 
144 


13.7  grains. 

OR, 

1  oz«  6  dwts.,  13.7  grains. 


176 


CARDINa  AND  DRAWING-TABLE. 


CARDING  AND  DRAWING-TABLE. 


From  .066  to  .11  decimal  of  hank  for  8  and  10  yards. 


Dec.  of 

8  yards. 

Dec.  of 

10  yards. 

oz. 

(Iwts. 

grains. 

oz. 

dvvts. 

grains. 

1  '^'^^ 

■i 

0 

lo.l 

.066 

2 

16 

3.6 

1  .067 

z 

■  0 

0. 

.067 

2 

15 

8.7 

1  -^^^ 

z 

4 

y.4 

.068 

2 

14 

14.4 

.069 

i 

6 

19.1 

.069 

2 

13 

20.7 

.07 

6 

O.d 

.07 

2 

13 

3.3 

.071 

z 

o 

-4 

15.9 

.071 

2 

12 

10.7 

.072 

z 

o 
Z 

2.9 

.072 

2 

1 1 

18.4 

.073 

z 

1 
1 

14.!<5 

.073 

2 

1 1 

2.5 

.074 

o 

z 

1 

Z. 

074 

2 

10 

11.1 

.075 

z 

U 

TOO 

.075 

2 

9 

20.1 

.076 

o 

z 

0 

z.z 

.076 

2 

9 

5.4 

.077 

17 

077 

2 

8 

15.2 

.078 

\ 

17 

n  o 
9.2 

.078 

2 

8 

1.3 

.079 

1  D 

22.  d 

.079 

2 

7 

11.8 

.08 

lb 

1  1  o 

11.8 

.08 

2 

6 

22.6 

.081 

1  D 

1.5 

.081 

2 

6 

9.8 

.082 

1  f) 

IRK 

10.5 

.082 

2 

5 

21.2 

.083 

1  0 

5.7 

.083 

2 

5 

9, 

.084 

j 

1 4 

2U.  1 

.084 

2 

4 

21. 

.085 

14 

10.8 

.085 

2 

4 

9.3 

.086 

14 

l.b 

.086 

2 

3 

21.8 

.087 

: 

Id 

lb. 7 

.087 

2 

3 

10.9 

.088 

: 

lo 

o 
o. 

.088 

2 

2 

23.3 

.089 

: 

1  o 
1 4 

.089 

2 

2 

13.2 

.09 

1^ 

15.2 

.09 

2 

2 

2.7 

.091 

} 

12 

7.1 

.091 

2 

1 

16.7 

.092 

11 

23.1 

.092 

2 

1 

6.3 

.093 

11 

15.3 

.093 

2 

0 

21. 

.094 

11 

7.7 

.094 

2 

0 

11.5 

.095 

11 

0.2 

.095 

2 

0 

2.1 

.096 

10 

16.9 

.096 

17 

22.5 

.097 

10 

9.7 

.097 

17 

13.6 

.098 

10 

2.7 

.098 

17 

4.8 

.099 

9 

19.9 

.099 

16 

20.2 

.1 

9 

13.1 

.1 

16 

11.8 

.102 

9 

0. 

.102 

15 

19.4 

.104 

8 

11.5 

.104 

15 

3.7 

.106 

7 

23.4 

.106 

14 

12.6 

.108 

7 

11.7 

.108 

13 

22.1 

.11 

7 

0.5 

.11 

13 

8. 

EXAMPLES.  5^  177 

When  the  proportion  or  decimal  of  the  hank  is  founcl,''-the''ft)l^ 
lowing  table  will  show  the  dividend  for  any  number  of  inches  in 
length,  from  1  to  36  inches,  when  the  quotient  will  be  the  weight 
in  grains: — 


Inches. 

Dividends. 

Inches. 

Dividends. 

1 

.23148 

19 

4.39812 

2 

.46296 

20 

4.6296 

3 

.69444 

21 

4.86108 

4 

.92592 

22 

5.09256 

5 

1.15740 

23 

5.32404 

6 

1.38888 

24 

5.55555 

7 

1.62036 

25 

5.787 

8 

1.85184 

26 

6.01848 

9 

2.08332 

27 

6.24996 

10 

2.3148 

28 

6.48144 

11 

2.54628 

29 

6.71292 

12 

2.77777 

30 

6.9444 

13 

3.00924 

31 

7.17588 

14 

3.24072 

32 

7.40736 

15 

3.4722 

33 

7.63884 

IG 

3.70368 

34 

7.87032 

17 

3.93516 

35 

8.1018 

18 

4.16666 

36 

8.3333 

N.  B. —  The  above  tables  will  shotv  the  dividends  for  any  number 
of  inches  of  lap,  or  cotton  fed  on  feed-cloth  at  laj)  machine  ; 
tlie  quotient  of  which  will  be  the  weight  in  grains  ;  the  divisor 
must  be  invariably  the  decimal,  or  proportion  of  the  hank. 

If  the  decimal,  or  proportion  of  the  hank  at  the  lap  machine, 
according  to  the  draught  and  doubling,  be  0.0005;  what  weight 
of  cotton  must  be  fed  on  12  inches  of  feed-cloth  at  lap  machine? 

Thus— Dec.  of  hank,  0.0005)2.7777  dividend  for  12  inches. 

5555.5  grains,  or  12  oz.,  12  dwts., 
17^  grains,  the  weight  of 
cotton  required. 

N".  B. —  The  loss  sustained  in  working  must  be  added  to  the  net 
weiglit  according  to  the  number  of  hanks  produced. 


178 


CARDING  AND  DRAWING-TABLE. 


CARDINa  AND  DRAWING-TABLE. 
From  .112  to  .24  decimal  of  hank  for  8  jmd  10  yards. 


Dec.  of 

S  yards. 

Bee.  of 

10  yards. 

oz. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

.112 

1 

X 

ft 

1,^  7 

.112 

1 

X 

X 

18  5 

XO . 

.114 

1 

6 

3.2 

.114 

1 

12 

5.4 

.116 

1 

ij 

17  9 

X  t 

.116 

1 

11 

16.8 

.118 

1 

*J 

7  4 

.118 

1 

11 

4  7 

12 

1 

A 

.12 

1 

10 

X  \J 

16.6 

.122 

1 

A 
rt 

12  9 

.122 

1 

1 0 

X  \J 

5.5 

.124 

1 

4 

4.2 

.124 

1 

9 

18.5 

.126 

1 

19  6 

.126 

1 

q 

7  8 

.128 

1 

3 

11.3 

.128 

1 

g 

21.5 

.13 

1 

3 

3.3 

.13 

1 

11.5 

.132 

1 

2 

19.5 

.132 

1 

8 

1.8 

.134 

1 

2 

12. 

.134 

1 

7 

15.6 

.136 

1 

2 

4  6 

.136 

1 

7 

* 

7.2 

.138 

1 

21.5 

.138 

1 

6 

22.3 

.14 

1 

14.6 

.14 

1 

6 

13.7 

.142 

1 

7  9 

1  • «-' 

.142 

1 

6 

5.3 

.144 

1 

1 

0.7 

.144 

1 

5 

21.2 

.146 

1 

0 

19. 1 

.146 

1 

5 

12.6 

.148 

1 

0 

12.9 

.148 

1 

5 

6. 

.15 

1 

0 

6.9 

.15 

1 

4 

22. 

.1525 

18 

5.1 

.1525 

1 

4 

12.9 

155 

17 

22.1 

.155 

1 

4 

4.1 

.1575 

1 7 

15.2 

.1575 

1 

3 

19.6 

.16 

1 7 

8.6 

.16 

1 

3 

11.3 

.165 

16 

X\J 

20 

.165 

1 

2 

19.5 

.17 

16 

8.1 

.17 

1 

2 

4.5 

.175 

15 

20.9 

.175 

1 

1 

14.6 

.18 

15 

10. 

.18 

1 

1 

1.4 

.185 

15 

0.3 

.185 

1 

0 

12.9 

.19 

14 

14.8 

.19 

1 

0 

1.1 

.195 

14 

5.8 

.195 

17 

19.3 

.2 

13 

21.3 

.2 

17 

8.6 

.205 

13 

13.2 

.205 

16 

22.5 

.21 

13 

5.4 

.21 

16 

12.8 

.215 

12 

22. 

.215 

16 

3.5 

.22 

12 

15. 

.22 

15 

18.7 

.225 

12 

8.2 

.225 

15 

10.3 

.23 

12 

1.8 

.23 

15 

2.3 

.235 

11 

19.6 

.235 

14 

18.6 

.24 

11 

13.7 

.24 

14 

11.2 

EXAMPLES. 


179 


If  8  yards  of  carding,  or  drawing  weigh  16  dwts.,  20  grains; 
what  proportion,  or  size  of  hank  will  it  be? 

Then  16  dwts.,  20  grains  are  equal  to  404  grains,  which  will 
be  the  divisor;  and  8  yards  are  of  a  lea,  or  66.666  grains, 
which  will  be  the  dividend. 

404)66.666(0.165  decimal,  or  proportion  of  hank, 
404  opposite  to  which  in  the  table 

  under  8  yards,  is  16  dwts.,  20 

2626  grains,  the  weight. 


2026 
2020 


6 

If  8  yards  of  carding  or  drawing  weigh  4  dwts.,  5  grains; 
what  proportion,  or  size  of  hank  will  it  be? 

4  dwts.,  5  grs,  are  equal  to  101  grs.)66. 666(0. 66  proportion,  or 

606  size  of  hank. 


606 
606 

What  will  8  yards  of  0.165  of  a  hank  of  carding,  or  drawing 
weigh  ? 

Then  8  yards  are  of  a  lea,  Avhich  is  equal  to  66.666  grains, 
which  will  be  the  dividend,  and  the  decimal  of  the  hank  0.165 
the  divisor. 

0.165)66.666(404  grains,  or  16  dwts.,  20  grains,  which 
660  will  be  found  in  the  column  under  8 

 yards;  to  the  left  hand  of  which  will 

666  be  found  0.165,  which  is  the  decimal, 
660        or  size  of  a  hank  for  8  yards  of  card- 

  ing  or  drawing  that  "weighs  16  dwts. 

6        20  grains. 


180 


CARDING  AND  DRAWING-TABLE. 


CAEDING  AND  DRAWING-TABLE. 


From  .245  to  .48  decimal  of  hank  for  8  and  10  yards. 


Dec.  of 

8  yards. 

Dec.  of 

10  yards. 

hank. 

grains. 

hank. 

grains. 

.245 

11 

8.1 

.245 

14 

4. 

.25 

11 

2.6 

.25 

13 

21.3 

.255 

10 

21.4 

.255 

13 

14.7 

.26 

10 

16.4 

.26 

13 

8.5 

.265 

10 

11.5 

.265 

13 

2.4 

.27 

10 

6.9 

.27 

12 

20.6 

.275 

10 

2.4 

.275 

12 

15. 

.28 

9 

22. 

.28 

12 

9.6 

.285 

9 

17.9 

.285 

12 

4.3 

.29 

9 

13.8 

.29 

11 

23.3 

.295 

9 

9.9 

.295 

11 

18.4 

.3 

9 

6.2 

.3 

11 

13.7 

.305 

9 

2.5 

.305 

11 

9.2 

.31 

8 

23. 

.31 

11 

4.8 

.315 

8 

19.6 

.315 

11 

0.5 

.32 

8 

16.3 

.32 

10 

20.4 

.325 

8 

13.1 

.325 

10 

16.4 

.33 

8 

10. 

.33 

10 

12.5 

.335 

8 

7. 

.335 

10 

8.7 

.34 

8 

4. 

.34 

10 

5. 

.345 

8 

1.2 

.345 

10 

1.5 

.35 

7 

22.4 

.35 

9 

22. 

.355 

.  7 

19.7 

.355 

9 

18.7 

.36 

7 

17.1 

.36 

9 

15.4 

.365 

7 

14.6 

.365 

9 

12.3 

.37 

7 

12.1 

.37 

9 

9.2 

.375 

7 

9.7 

.375 

9 

6.2 

.38 

7 

7.4 

.38 

9 

3.3 

.385 

7 

5.1 

.385 

9 

0.4 

.39 

7 

2.9 

.39 

8 

21.6 

.395 

1 

0.7 

.395 

8 

18.9 

.4 

6 

22.6 

.4 

8 

16.3 

.41 

6 

18.6 

.41 

8 

11.2 

.42 

6 

14.7 

.42 

8 

6.4 

.43 

6 

11. 

.43 

8 

1.8 

.44 

6 

7.5 

.44 

7 

21.3 

.45 

6 

4.1 

.45 

7 

17.1 

.46 

6 

0.9 

.46 

7 

13.1 

.47 

5 

21.8 

.47 

7 

9.3 

.48 

5 

18.8 

.48 

7 

5.6 

EXAMPLES. 


181 


What  will  18  yards  of  IJ  hank  slabbing  weigh? 

Then  18  yards  is  ^^j,  of  a  lea,  or  120  yards,  which  is  equal  to 
150  grains  of  a  1  hank,  which,  divided  by  1^,  or  1.25,  will  give 
the  weight  in  grains  that  18  yards  should  weigh. 

Grains. 

Hank  slabbing  1,25)150.0(120  grains,  or  5  dwts.,  weight 
125  required. 


250 
250 

If  18  yards  of  slabbing  weigh  5  dwts.,  or  120  grains ;  what 
hank  will  it  be? 

120)150.00(1.25  hank  slabbing. 

120 


300 
240 


600 
600 

What  will  37  yards  of  If  hank  slabbing  weigh? 

Then  37  yards  is  of  a  lea,  or  120  yards,  which  is  equal  to 
308.333  grains  of  a  1  hank,  which,  divided  by  If,  or  1.75,  will 
give  the  weight  in  grains  that  37  yards  should  weigh. 

1.75)308.3333(176.19  grains,  or  7  dwts.,  8.19 
175  grs.,  weight  required. 


1333 
1225 


1083 
1050 


333 
175 


1583 
1575 


182  GARBING,  DRAWING,  AND  SLABBING-TABLE. 


CARDINa,  DRAWING,  AND  SLABBING-TABLE. 
From  .5  to  .99  decimal  of  hank  for  8,  10,  and  20  yards. 


Dec.  of 
hank. 

8  yards. 

Dec.  of 
hank. 

10  yards. 

Dec.  of 
hank. 

20  yards. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

.5 

5 

13.3 

.5 

6 

22.6 

.5 

13 

21.2 

.51 

5 

10.7 

.51 

6 

19.4 

.51 

13 

14.8 

.52 

5 

8.2 

.52 

6 

16.2 

.52 

13 

8.4 

c  o 
.00 

5 

5.7 

.53 

6 

13.2 

.53 

13 

2.4 

.54 

5 

3.4 

.54 

6 

10.3 

.54 

12 

20.6 

.55 

5 

1.2 

.55 

6 

7.5 

.55 

12 

15. 

.5b 

4 

23. 

.56 

6 

4.8 

.56 

12 

9.6 

.57 

4 

20.9 

.57 

6 

2.2 

.57 

12 

4.4 

.00 

4 

18.9 

.58 

5 

23.6 

.58 

11 

23.2 

.59 

4 

17. 

.59 

5 

21.2 

.59 

11 

18.4 

.0 

4 

15.1 

.6 

5 

18.8 

.6 

11 

13.6 

.02 

4 

11.5 

.02 

5 

14.4 

n  o 

.62 

11 

4.8 

.04 

4 

8.1 

.b4 

5 

10.2 

.64 

10 

20.4 

p  f* 

.OD 

4 

5. 

.00 

5 

6. 

.66 

10 

12. 

f*o 
.ob 

4 

2. 

.bo 

5 

2.5 

.68 

10 

5. 

.7 

3 

23.2 

.7 

4 

23. 

.7 

9 

22. 

.  /2 

3 

20.6 

.72 

4 

19.6 

.72 

9 

15.2 

3 

18. 

.  <4 

4 

16.6 

.74 

9 

9.2 

.7o 

3 

15.7 

Ti^ 

.75 

4 

13.6 

T  C* 

.  /D 

9 

3.2 

*-'  O 

.10 

3 

13.4 

.  /8 

4 

10.8 

.  /  8 

8 

21.6 

o 
.0 

3 

11.3 

D 

.0 

4 

8.1 

o 

.8 

8 

16.2 

3 

10.3 

o  1 

.oi 

4 

6.8 

O  1 

.81 

8 

13.7 

3 

9.3 

O.I 

.o2 

4 

5.6 

.oz 

8 

11.2 

o  o 
.oo 

3 

8.2 

.83 

4 

4.3 

.83 

8 

8.8 

o  ,i 
.o4 

3 

7.3 

O  ( 

.o4 

4 

3.2 

.84 

8 

6.4 

.00 

3 

6.4 

o  ^ 
.00 

4 

2. 

.85 

8 

4. 

or* 
.00 

3 

5.5 

.bo 

4 

0.9 

.86 

8 

1.8 

.87 

3 

4.6 

.87 

3 

23.7 

.87 

7 

23^5 

.88 

3 

3.7 

.88 

3 

22.7 

.88 

7 

21.4 

.89 

3 

2.9 

.89 

3 

21.6 

.89 

7 

19.2 

.9 

3 

2. 

.9 

3 

20.6 

.9 

7 

17.2 

.91 

3 

1.2 

.91 

3 

19.5 

.91 

7 

15.1 

.92 

3 

0.4 

.92 

3 

18.6 

.92 

7 

13.2 

.93 

3 

23.6 

.93 

3 

17.5 

.93 

7 

11.2 

.94 

2 

23. 

.94 

3 

16.6 

.94 

7 

9.2 

.95 

2 

22.1 

.95 

3 

15.6 

.95 

7 

7.3 

.96 

2 

21.4 

.96 

3 

14.8 

.96 

7 

5.6 

.97 

2 

20.7 

.97 

3 

13.9 

.97 

7 

3.8 

.98 

2 

20. 

.98 

3 

13. 

.98 

7 

2. 

.99 

2 

19.3 

.99 

3 

12.1 

.99 

7 

o's 

EXAMPLES. 


183 


The  slabbing  and  roving  tables  rise  progressively  in  20th  parts 
of  a  hank,  as  will  be  seen  in  the  following  tables.  Thus  1,  1.05, 
or  Ij'o  and  so  on  to  2  and  3  hank,  &c. 

What  will  20  yards  of  IJ,  or  1.25  hank  slabbing  weigh? 

Then  20_yards  is  i  of  a  lea,  or  120  yards,  which  is  equal  to 
166.66  grains  of  a  1  hank,  as  shown  in  a  preceding  table;  which, 
divided  by  IJ,  or  1.25,  will  give  the  weight  in  grains  that  20 
yards  should  weigh. 

Grains. 

Hank  slabbing,  1.25)166.66(133 
125 


416 
375 


416 
375 


416 
375 


416 
375 

41 

If  20  yards  of  slabbing  weigh  5  dwts.,  13.3  grains;  what  hank 
will  it  be  ? 

5  dwts.,  13.3  grains  =  133.33)166.66(1.25,  or  1+  hank  slabbing. 

13333 


33336 
26666 

66706 
66666 


.33,  or  5  dwts.  13/o  grs.  weight, 
which  will  be  found  in  the 
table  opposite  1.25,  and 
under  20  yards. 


40 


184 


SLABBING  AND  ROVING-TABLE, 


SLABBING  AND  ROVING-TABLE. 

From  1  hauk  to  2.95  hanks  for  20,  30,  40,  and  60  yards. 


! 

Hank 

20  yards. 

30  yards. 

40  yards. 

60  yards.  j 

roving.  [ 

dvvts. 

grains. 

oz. 

dwts. 

grains. 

dwts. 

grains. 

oz. 

dwts. 

grams.  1 

1. 

6 

22.6 

10 

10. 

13 

21.3 

1 

2 

14.5  I 

i.UO 

6 

14.7 

9 

22. 

13 

5.4 

1 

1 

14.7 

l.i 

0 

7.5 

9 

11.2 

!o 

15. 

1 

0 

17. 

i.io 

6 

0.9 

9 

1.3 

12 

1.8 

18 

2.7 

1  O 

L.Z 

5 

18.8 

8 

16.3 

11 

13.7 

17 

8.6 

i.zo 

5 

13.3 

8 

8. 

11 

2.6 

16 

16. 

i.o 

5 

8.2 

8 

0.3 

10 

16.4 

16 

0.6 

i.rfo 

5 

3.4 

7 

17.1 

10 

6.9 

15 

10.3 

1.4 

4 

23. 

7 

10.5 

9 

22. 

14 

21.1 

1.45 

4 

18.9 

7 

4.4 

9 

13.8 

14 

8.8 

i.o 

4 

15.1 

6 

22.6 

9 

6.2 

13 

21.3 

1.00 

4 

11.5 

6 

17.2 

8 

23. 

13 

10.5 

I.o 

4 

8.1 

o 

12.2 

8 

16.3 

13 

0.5 

l.DO 

4 

5.1 

0 

7.6 

8 

10.2 

12 

15. 

1.7 

4 

2 

b 

3. 

8 

4. 

12 

6.1 

1.7o 

3 

23.9 

5 

22.8 

7 

22.4 

11 

21.7 

1.0 

3 

20.6 

5 

18.8 

7 

17.1 

11 

13.7 

l.OO 

3 

18. 

r 

0 

15.1 

7 

12.1 

11 

6.2 

1.9 

3 

15.7 

r 

0 

11.5 

7 

7.4 

10 

23.1 

1.90 

3 

13.4 

5 

8.2 

7 

2.9 

10 

16.4 

3 

11.3 

5 

5. 

6 

22.6 

10 

10. 

2.UD 

3 

9.3 

5 

1.9 

6 

18.6 

10 

3.8 

2.1 

3 

7.3 

4 

23. 

6 

14.7 

9 

22. 

2.15 

3 

5.5 

4 

20.2 

6 

11. 

9 

16.4 

2.2 

3 

3.7 

4 

17.6 

6 

7.5 

9 

11.3 

2.25 

3 

2_ 

4 

15.1 

6 

4.1 

9 

6.2 

2.3 

3 

0'4 

4 

12.6 

6 

0.9 

9 

1.3 

2.35 

2 

22.9 

4 

10.3 

5 

21.8 

8 

10'6 

2.4 

2 

21.4 

4 

8.1 

5 

18.8 

8 

16.2 

2.45 

2 

20. 

4 

G. 

5 

16. 

8 

12. 

2.5 

2 

18.6 

4 

4. 

5 

13.3 

8 

8. 

2.55 

2 

17.3 

4 

2. 

5 

10.7 

8 

4. 

2.6 

2 

16.1 

4 

0.1 

5 

8.2 

8 

0.3 

2.G5 

2 

14.9 

3 

22.3 

5 

5.7 

7 

20.6 

2.7 

2 

13.7 

3 

20.6 

5 

3.4 

7 

17.2 

2.75 

2 

12.6 

3 

18.9 

5 

1.2 

7 

13.8 

2.8 

2 

11.5 

3 

17.2 

4 

23. 

7 

10.5 

2.85 

2 

10.4 

3 

15.7 

4 

20.9 

7 

7.4 

2.9 

2 

9.4 

3 

14.2 

4 

18.9 

7 

4.4 

2.95 

2 

8.5 

3 

12.7 

4 

17. 

7 

1.5 

EXAMPLES.  185 

What  will  30  yards  of  2/^  hank  roving  weigh? 

250  is  the  dividend  for  30  yards,  which  must  be  divided  by  the 
hank  roving,  and  the  quotient  will  be  the  weight  in  grains. 

Hank  roving,  2.9)250(86.2  grains,  or  3  dwts.,  14.2  grs.,  which 
232  will  be  found  in  the  table  under  30 
- — r-T-      yards,  and  opposite  2.9  in  the  co- 

180       lumn  of  the  hank  roving. 

174 


60 
58 


2 

If  40  yards  weigh  4  dwts.,  5  grains;  what  hank-roving  will 
it  be? 

4  dwts.,  5  grains,  =  101  grs.)333.33(3.3,  or  Sj%  hank-roving. , 

303 


303 
303 

What  will  60  yards  of  3f,  or  3.75  hank-roving  weigh? 

500  is  the  dividend  for  60  yards. 

Hank-roving  3f,  or  3.75)500.00(133.3,  or  5  dwis.,  13.3  grs.^ 

375  weight  of  60  yards  of 

  a  3|  hknk-roving. 

1250 
1125 


1250 
1125 


1250 
1125 


125 

13 


186 


ROVING-TABLE. 


ROVING-TABLE. 


From  3  hank,  to  7.25  hanks,  for  20,  30,  40,  and  60  yards. 


1 

j  Hank 

20  yards. 

30  yards. 

1       40  yards. 

1 

60  yards.  1 

roving. 

dwts. 

grains. 

dwts 

1  grains. 

j  dwts. 

grains. 

dwts. 

1  grains. 

3. 

2 

7.5 

3 



11.3 

4 

15.1 

6 

22.6 

3.05 

2 

6.6 

3 

9.9 

4 

13.2 

6 

19.9 

3.1 

2 

5.7 

3 

8.6 

4 

11.5 

6 

16.3 

3.15 

2 

4.9 

3 

7.3 

4 

9.8 

6 

14.7 

3.2 

2 

4. 

3 

6.1 

4 

8.1 

6 

12.2 

3.25 

2 

3.2 

3 

4.9 

4 

6.5 

6 

9.8 

3.3 

2 

2.5 

3 

3.7 

4 

5. 

6 

7.5 

3.35 

2 

1.7 

3 

2.6 

4 

3.5 

6 

5.2 

3.4 

2 

1. 

3 

1.5 

4 

2. 

6 

3. 

3.45 

2 

0.3 

3 

0.4 

4 

0.6 

6 

0.9 

3.5 

1 

23.6 

2 

23.4 

3 

22.2 

5 

22.8 

3.55 

1 

22.9 

2 

22.4 

3 

21.9 

5 

20.8 

3.6 

1 

22.3 

2 

21.4 

3 

20.6 

5 

18.8 

3.65 

1 

21.6 

2 

20.5 

8 

19.3 

5 

16.9 

3.7 

1 

21. 

2 

19.5 

3 

18.1 

5 

15.1 

3.75 

1 

20.4 

2 

18.6 

3 

16.8 

5 

13.3 

3.8 

1 

19.8 

2 

17.7 

3 

15.7 

5 

11.5 

3.85 

1 

19.2 

2 

16.9 

3 

14.5 

5 

9.9 

3.9 

1 

18.7 

2 

16.1 

3 

13.4 

5 

8.2 

3.95 

1 

18.1 

2 

15.3 

3 

12.4 

5 

6.6 

4. 

1 

17.6 

2 

14.5 

3 

1].3 

5 

5. 

4.1 

1 

16.6 

2 

12.9 

3 

9.3 

5 

1.9 

4.2 

1 

15.7 

2 

11.5 

3 

7.3 

4 

23. 

4.3 

1 

14.7 

2 

10.1 

3 

5.5 

4 

20.2 

4.4 

1 

13.8 

2 

8.8 

3 

3.7 

4 

17.6 

4.5 

13. 

2 

7.5 

3 

2. 

4 

15.1 

4.6 

} 

12.2 

2 

6.3 

3 

0.4 

4 

12.7 

4.7 

111 
1 1  .-± 

2 

9 

99  Q 

Tt 

4.8 

10.7 

2 

4.1 

2 

21.4 

4 

8.1 

4.9 

10. 

2 

3. 

2 

20. 

4 

6. 

b. 

9.3 

2 

2. 

2 

18.6 

4 

4. 

5.25 

7.6 

23.6 

2 

15.2 

o 
O 

23.2 

5.5 

6.3 

21.4 

2 

12.6 

3 

18.9 

5.75 

4.9 

19.5 

2 

9.9 

3 

15. 

6. 

3.7 

17.6 

2 

7.5 

3 

11.3 

6.25 

2.6 

16. 

2 

5.3 

3 

8. 

6.5 

1.6 

14.4 

2 

3.2 

3 

4.9 

6.75 

O.G 

13. 

2 

1.3 

o 
O 

2. 

7. 

23.8 

11.7 

1 

23.6 

2 

23.4 

7.25 

22.9 

10.4 

1 

21.9 

2 

20.9 

ROVING-FRAME. 


18T 


CHANGE-PINIONS  AT  ROVING-FRAME. 

By  changing  the  driving-wheels,  less  pinions  produce  finer 
roving,  by  increasing  the  draught  in  rollers :  driven-wheels  de- 
crease the  hank-roving  by  reducing  the  draught  in  the  rollers. 
RULE. — Multiply  the  hank-roving  by  the  number  of  teeth  in  the 
change-wheel,  or  pinion,  and  divide  by  the  hank-roving  you 
want,  and  the  quotient  will  be  the  change-wheel,  or  pinion  re- 
quired. 

If  a  4  hank-roving  requires  a  24  teeth  change-wheel,  or  pinion ; 
what  will  a  4|  hank  require? 

4  hank-roving. 

24  teeth,  change-wheel,  or  pinion. 

Hank-rov.  required,  4.75)96.00(20.21,  or  20  teeth,  change-pinion, 

9500  being  a  driving-wheel. 


1000 
950 


500 
475 


25 

If  a  4  hank-roving  requires  a  48  teeth  (driven)  change-wheel, 
or  pinion ;  what  will  a  4^  hank  require  ? 

4  hank-roving. 
48  teeth,  change-wheel. 


Hank-rov.  required,  4.25)192.00(45.17,  or  45  teeth,  change-whl. 

1700  or  pinion  required,  being 

■   a  driven-wheel. 

2200 
2125 


750 

425 


3250 
2975 


275 

B.—It  seldom  occurs  that  a  change-wheel  can  he  had  to  pro- 
duce exactly  what  is  wanted. 


188 


ROVING-TABLE. 


ROVING-TABLE. 


From  7.5  to  18.5  hanks  for  30,  40,  60,  and  120  yards. 


Dec.  of 
hank. 

30  yards. 

40  yards. 

60  yards. 

120  yards  or  1  lea. 

dwts. 

grains. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

7.5 

1 

9.3 

1 



20.4 

2 

18.6 

5 

13.3 

7.75 

1 

8.2 

1 

19. 

2 

16.5 

5 

9. 

8. 

1 

7.2 

1 

17.6 

2 

14.5 

5 

5. 

8.25 

1 

6.3 

1 

16.4 

2 

12.6 

5 

1.2 

8.5 

1 

5.4 

1 

15.2 

2 

10.8 

4 

21.6 

8.75 

1 

4.5 

1 

14.1 

2 

9.1 

4 

18.2 

9. 

1 

3.7 

1 

13. 

2 

7.5 

4 

15.1 

9.25 

1 

3. 

1 

12. 

2 

6. 

4 

12. 

9.5 

1 

2.3 

1 

11.1 

2 

4.6 

4 

9.2 

9.75 

1 

1.6 

1 

10.1 

2 

3.2 

4 

6.4 

10. 

1 

1. 

1 

9.33 

2 

2. 

4 

4. 

10.25 

1 

0.39 

1 

8.52 

2 

0.78 

4 

1.56 

10.5 

23.81 

1 

7.73 

1 

23.62 

3 

23.23 

10.75 

23.26 

1 

7. 

1 

22.52 

3 

21.04 

11. 

22.72 

1 

6.3 

1 

22.15 

3 

18.9 

11.25 

22.22 

1 

5,62 

1 

20.44 

3 

16.88 

11.5 

21.73 

1 

4.98 

1 

19.47 

3 

14.95 

11.75 

21.27 

1 

4.33 

1 

18.55 

3 

13.1 

12. 

20.83 

1 

3.77 

1 

17.66 

3 

11.33 

12.25 

20.4 

1 

3.2 

1 

16.81 

3 

9.6 

12.5 

20. 

1 

2.66 

1 

16. 

3 

8. 

12.75 

19.6 

1 

2.14 

1 

15.21 

3 

6.43 

13. 

19.23 

1 

1.64 

1 

14.46 

3 

4.92 

13.25 

18.86 

1 

1.16 

1 

13.73 

3 

3.47 

13.5 

18.51 

1 

0.69 

1 

13.03 

3 

2.07 

13.75 

18.18 

1 

0.24 

1 

12.36 

3 

0.72 

14. 

17.85 

23.8 

1 

11.71 

2 

23.42 

14.25 

i  /  .04: 

T 

X 

0 

14.5 

17.24 

22.98 

1 

10.48 

2 

20.96 

14.75 

16.94 

22.89 

1 

9.89 

2 

19.79 

15. 

16.66 

22.22 

1 

9.33 

2 

18.66 

15.25 

16.39 

21.85 

1 

8.78 

2 

17.57 

15.5 

16.12 

21.52 

1 

8.25 

2 

16.57 

15.75 

15.87 

21.16 

1 

7.74 

2 

15.49 

16. 

15.62 

20.83 

1 

7.25 

2 

14.5 

16.5 

15.15 

20.2 

1 

6.3 

2 

12.6 

17. 

14.7 

19.6 

1 

5.41 

2 

10.82 

17.5 

14.28 

19.05 

1 

4.57 

2 

9.14 

18. 

13.88 

18.51 

1 

3.77 

2 

7.55 

18.5 

13.51 

18.01 

1 

3.02 

2 

6.05 

EXAMPLES. 


189 


If  30  yards  of  roving,  with  a  24  teeth  change-wheel,  weigh  2 
dwts.,  14|  grains;  what  number  of  grains  will  the  same  length 
weigh  with  a  22  teeth  change-wheel  (driving)  ? 
2  dwts.,  141  grs.,  =  62.5  grs.,  weight  of  30  yds.  with  24  tth.  whl. 
22  teeth  change-wheel. 


1250 
1250 


Chn.  whl.  24  tth.)1375.0(57.29,  or  2  dwts.,  9|-  grains. 
120 


175 
168 


70 

48 


220 
216 


4 

If  62^  grains  of  roving  require  a  24  teeth  change-wheel,  or 
pinion;  what  change-wheel,  or  pinion  will  there  be  required  to 
produce  a  hank-roving  the  same  length  which  will  weigh  57  J 
grains? 

57.25  grains,  weight  required. 

24  teeth,  change-pinion,  or  wheel. 

22900 
11450 


Given  weight,  62.5  grs.)  1374.00(22  teeth,  nearly,  change-wheel, 
1250  or  pinion  required. 


1240 

1250 — nearly. 

B. —  Whe7t  the  number  of  grains  which  any  given  length 
weighs,  is  taken  instead  of  the  hank,  multiply  the  grains  by 
the  cha7ige-wheel,  or  pinion  you  intend  putting  on,  and  divide 
by  the  change-ivheel  you  have  working,  and  the  quotient  will  be 
the  weight  in  grains  required. 


190 


EXAMPLES. 


The  following  -will  be  the  dividends  for  any  number  of  leas, 
from  1  to  7  leas,  or  1  hank : — 

iV.  B. — For  as  many  leas  that  you  weigTi,  take  as  many  thousands 
for  your  dividend,  as  shown  in  the  annexed  table  of  dividends. 


Leas. 

Dividends. 

1 

1000 

2 

2000 

3 

3000 

4 

4000 

5 

5000 

6 

6000 

7 

7000 

What  will  2  leas  of  22J  hank-roving,  or  yarn  weigh  ? 

Hank-roving,  or  yarn,  22.5)2000.0(88.888  grs,  or  3  dwts.  16.88 

1800  grains. 


2000 
1800 


2000 
1800 


2000 
1800 


2000 
1800 


200 

If  2  leas  weigh  8  dwts.,  17  grains ;  what  hank  will  it  be  ? 

3  dwts.,  17  grains  =  89  grs.)2000(22.5,  or  22*  hanks,  nearly. 

178 


220 
178 


420 

445 — nearly. 


ROVING  AND  YARN-TABLE. 


191 


ROVINa  AND  YARN-TABLE. 


From  19  to  33.5  hanks  for  1,  2,  3,  and  4  leas. 


Hank 
roving. 

1 

lea. 

2  leas. 

3  leas. 

4  leas. 

dwts. 

grains. 

oz. 

1  dwts. 

1 

1  grains. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

19. 

2 

4.63 

4 

9.26 

6 

13.89 

8 

18.52 

19.5 

2 

2.28 

4 

6.56 

6 

9.84 

8 

13.12 

20. 

2 

2. 

4 

4. 

6 

6. 

8 

8. 

20.5 

2 

0.'78 

4 

1.56 

6 

2.34 

8 

3.12 

21. 

1 

23.61 

3 

23.23 

5 

22.85 

7 

22.47 

21.5 

1 

22.51 

3 

21.02 

5 

19.53 

7 

18.40 

22. 

1 

21.45 

3 

18.9 

5 

16.36 

7 

13.81 

22.5 

1 

20.44 

3 

16.88 

5 

13.33 

7 

9.77 

23. 

1 

19.47 

3 

14.95 

5 

10.43 

7 

5.61 

23.5 

1 

18.55 

3 

13.1 

5 

7.65 

7 

2.2 

24. 

1 

17.66 

3 

11.33 

5 

5. 

6 

22.6 

24.5 

1 

16.81 

3 

9.63 

5 

2.44 

6 

19.26 

25. 

1 

16. 

3 

8. 

5 

0. 

6 

16. 

25.5 

1 

15.21 

3 

6.43 

4 

21.64 

6 

12.86 

26. 

1 

14.46 

3 

4.92 

4 

19.38 

6 

9.84 

26.5 

1 

13.73 

3 

3.47 

4 

17.2 

6 

6.94 

27. 

1 

13.03 

s 

2.07 

4 

lo.ll 

r* 

o 

4.14 

27.5 

1 

12.36 

3 

0.72 

4 

13.09 

6 

1.44 

zo. 

11  71 
1 1.  /  1 

2 

23.42 

4 

11.14 

5 

22.85 

28.5 

1 

11.08 

2 

22.17 

4 

9.26 

5 

20.34 

29. 

1 

10.48 

2 

20.96 

4 

7.44 

5 

17.93 

29.5 

1 

9.89 

2 

19.79 

4 

5.09 

5 

15.58 

30. 

1 

9.33 

o 

18.66 

4 

4. 

5 

13.33 

30.5 

1 

8.78 

2 

17.57 

4 

2.36 

5 

11.14 

31. 

1 

8.25 

o 
^ 

16.51 

4 

0.76 

5 

9.03 

31.5 

1 

7.74 

2 

15.39 

3 

23.23 

5 

6.78 

32. 

1 

7.22 

2 

14.5 

3 

21.75 

5 

5. 

32.5 

1 

676 

2 

13.53 

3 

20.3 

5 

3.16 

33. 

1 

6.3 

2 

12.6 

3 

18.9 

5 

1.21 

33.5 

1 

5.85 

2 

11.7 

8 

17.55 

4 

23.4 

For  Yarn-Tables  from  IVo.  1  to  300,  and  from  1  to  7  leas,  and 
10  hanks  in  length,  see  Tables  published  by  Robert  Scott. 


192  SELF-ACTING  MULES. 


SELF-ACTING  MULES. 

The  speed  of  the  twist-shaft  is  required  from  the  following 
particulars: — 

Revolutions  of  lying-shaft  a  minute,  136. 
Diameter  of  drum  on  shaft,  21  inches. 
Diameter  of  pulley  on  counter-shaft,  14  inches. 
Diameter  of  drum  on  counter-shaft,  16  inches. 
Diameter  of  pulleys  on  twist-shaft,  12  inches. 

136  revolutions  of  lying-shaft  a  minute. 
21  inches,  diameter  of  drum  on  lying-shaft. 


136 
272 


2856 

16  inches,  diam.  of  drum  on  counter-shaft. 


17136 

2856 


45696  dividend. 

14  inches,  diam.  of  pulley  on  counter-shaft- 
12  inches,  diam.  of  pulleys  on  twist-shaft. 


168  divisor. 

168)45696(272  revolutions  of  twist-shaft  a  min. 
336 


1209 
1176 


336 
336 

iV.  B. —  The  self-acting  mules  from  widch  these  calculations  are 
made,  are  spinning  numbers  36's  pin  cops  for  power  loom 
weaving. 

The  speed  of  the  spindles  is  required  from  the  following  par- 
ticulars : — 


SELF-ACTING  MULES. 


193 


Revolutions  of  twist-shaft  a  minute,  272. 
Diameter  of  grooved  pulley  on  tAvist-shaft,  17§  inches. 
Diameter  of  grooved  twist-pulley  for  driving  vertical  shaft,  10|- 
inches. 

Diameter  of  grooved  pulley  on  vertical  shaft,  10 J  inches. 
Diameter  of  grooved  pulley  on  tin  drums,  10  inches. 
Diameter  of  tin  drums,  driving  spindles,  10  inches. 
Diameter  of  spindle-wharves,  ^  inch. 

JV.  jB. —  ITiere  are  generally  3  grooves  in  the  hand-pulley  on  the 
twist-shaft,  the  diameters  of  which  are  17  f,  18,  and  18f  inches. 

When  the  driving  and  driven-pulleys,  or  drums,  are  alternately 
of  the  same  dimensions  as  in  the  above  question,  they  are  omitted 
in  the  work. 


272  revolutions  of  twist-shaft  a  minute. 
17.375,  or  17f  inches,  diameter  of  groove  in 


1360 
1904 
816 

1904 

272 


4726.000  dividend. 


The  divisor  will  be  .875,  which  is  equal  to  7-8ths  of  an  inch, 
the  diameter  of  the  spindle-wharves. 


.875)4726.000(5401.1428  revolutions  of  spindles 


pulley  on  twist-shaft. 


4375 


a  minute. 


3510 
3500 


1000 
875 


1250 
875 


2500 
1750 


3750 
3500 


7500 
7000 


194 


SELF-ACTING  MULES. 


The  speed  of  the  vertical  shaft  is  required  from  the  following 
particulars: — 

Revolutions  of  twist-shaft  a  minute,  272. 
Diameter  of  groove  in  pulley  on  twist-shaft,  17f  inches. 
Diameter  of  grooved  twist-pulley  for  driving  vertical-shaft,  lOj 
inches. 

272  revolutions  of  twist-shaft  a  minute. 
17.375,  or  17f  inches,  diameter  of  groove  in 

  pulley  on  twist-shaft. 

1360 
1904 
816 
1904 
272 


4726.000  dividend. 

The  divisor  will  be  10.25,  or  lOJ  inches,  the  diameter  of  the 
grooved  twist-pulley  for  driving  vertical  shaft. 

10.25)4726.00(461.07317  revolutions  of  vertical  shaft 
4100  a  minute. 

6260 
6150 

1100 
1025 

7500 
7175 

3250 
3075 

1750 
1025 

7250 
7175 


75 


SELF-ACTING  MULES. 


195 


W.  B. — There  is  a  40  teeth-ioheel  on  the  grooved  twist-pulley- 
shaft,  which  works  into  a  40  teeth-wheel  on  the  foot  of  the  ver- 
tical-shaft; but  one  being  a  driving  and  the  other  a  driven- 
wheel,  and  each  containing  the  same  number  of  teeth,  they  are 
omitted  in  the  above  question  and  example. 

The  speed  of  the  front  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  twist-shaft  a  minute,  272. 

Back  pinion  on  twist-shaft,  18  teeth. 

Back  intermediate  wheel,  42  teeth. 

Back  adjustable  intermediate  wheel,  70  teeth. 

Back  change-wheel  on  back-shaft,  50  teeth. 

Wheel  on  back-shaft  driving  front  rollers,  40  teeth. 

Wheel  on  front  rollers,  connected  with  catch-box,  40  tth. 

272  revolutions  of  twist-shaft  a  minute. 
18  teeth,  back  pinion  on  twist-shaft. 

2176 
272 


4896  dividend. 

The  divisor  will  be  50,  being  the  number  of  teeth  in  the  change- 
wheel  on  the  back-shaft.  All  the  other  wheels,  with  the  exception 
of  the  back  pinion  on  the  twist-shaft,  are  omitted,  on  account  of 
being  connecting,  or  driving  and  driven-wheels  containing  the 
same  number  of  teeth. 

5.0)489.6 

97.92  revols.  of  front  rollers  a  minute. 

If  the  front  rollers  at  the  mules  be  1  inch  diameter,  making 
97.92  revolutions  a  minute;  how  many  inches  will  they  traverse  ? 

3.1416  circumference  when  the  diameter  is  1. 
97.92  revolutions  of  front  rollers  a  minute. 


62832 
282744 
219912 
282744 


307.625472  inches,  front  rollers  traverse  a  minute. 


JC 


196 


SELF-ACTING  MULES. 


The  speed  of  the  middle  rollers  is  required  from  the  following 
particulars : — 

Revolutions  of  front  rollers  a  minute,  97.92, 

Wheel  on  the  front  rollers,  20  teeth. 

Crown-wheel,  108  teeth. 

Change-pinion,  24  teeth. 

Wheel  on  the  back  rollers,  50  teeth. 

Wheel  on  the  end  of  back  rollers,  working  into  stud-wheel  which 

drives  middle  rollers,  32  teeth. 
Wheel  on  the  middle  rollers,  25  teeth. 

97.92  revolutions  of  front  rollers  a  minute. 
20  teeth,  wheel  front  rollers. 


1958.40 

24  teeth,  change-pinion. 


78336 
39168 


47001.6 


32  teeth,  wheel  on  the  end  of  back  rollers. 


940032 
1410048 


1504051.2  dividend. 


108  teeth,  crown-wheel. 

50  teeth,  wheel  on  the  back  rollers. 


5400 

25  teeth,  wheel  on  the  middle  rollers. 


27000 
10800 


135000  divisor. 
f5)1504.051.2 

5  xfx  3=^35  i 


1^  3)33.42336 


11.14112  revolutions  of  middle  rollers  a 
minute. 


i 


SELF-ACTING  MULES. 


197- 


If  the  middle  rollers  be  f  of  an  inch  diameter,  making  11.14112 
revolutions  a  minute;  how  many  inches  will  they  traverse  ? 

11.14112  revolutions  of  middle  rollers  a  min. 
.75  or  f  inch  diameter  of  middle  rollers. 

5570560 
7798784 


8.3558400 

3.1416  circumference  when  the  diameter  is  1. 


5013504 
835584 

3342336 

835584 
2506752 


26.250706944,  or  rather  more  than  26|  inches,  mid- 
dle rollers  traverse  a  minute. 
The  speed  of  the  back  rollers  is  required  from  the  following 
particulars: — 

Revolutions  of  the  front  rollers  a  minute,  97.92. 

Wheel  on  the  front  rollers,  20  teeth. 

Crown-wheel,  108  teeth. 

Change-pinion,  24  teeth. 

Wheel  on  the  back  rollers,  50  teeth. 

97.92  revolutions  of  front  rollers  a  minute. 
20  teeth,  wheel  on  front  rollers. 


1958.40 

24  teeth,  change-pinion. 


78336 
39168 


47001.6  dividend. 
108  teeth,  crown  wheel. 

50  teeth,  -wheel  on  the  back  rollers. 

^77^  A-  ■  (9)470.01.6 
54.00  divisor,  or  J  J_  

9  X  6  =  54     I  6)52.224 


8.704  revolutions  of  back  rol- 
lers a  minute. 


198 


SELF-ACTING  MULES. 


If  the  back  rollers  be  |ths  of  an  inch  diameter,  making  8.704 
revolutions  a  minute ;  how  many  inches  will  they  traverse  ? 

8.704  revolutions  of  back  rollers  a  minute. 
.875,  or  '^ths  of  an  inch,  diam.  of  rollers. 


43520 
60928 
69632 


7.616000 

3.1416  circumference  when  the  diameter  is  1. 


45696 
7616 

80464 

7616 
22848 


23.9264256,  or  nearly  24  inches,  back  rollers  traverse 
a  minute. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars  : — 

Middle  rollers  traverse  26.250706944  inches  a  minute. 
Back  rollers  traverse  23.9264256  inches  a  minute. 
23.9264256)26.250706944(1.0971428,  or  nearly  l^'g  draught 
239264256  between  the  mid.  and 

 back  rols. 

2324281344 
2153378304 


1709030400 
1674849792 


341806080 
239264256 


1025418240 
957057024 


683612160 
478528512 


2050836480 
1914114048 


136722432 


SELF-ACTING  MULES. 


199 


The  draught  between  the  front  and  middle  rollers  is  required 
from  the  following  particulars  : — ■ 

Front  rollers  traverse  307.625472  inches  a  minute. 
Middle  rollers  traverse  26.250706944  inches  a  minute, 
26.250706944)307.62547200(11.71875  draught  between  the 
26250706944  front  and  mid.rollers. 


45118402560 
26250706944 


188676956160 
183754948608 


49220075520 
26250706944 


229693685760 
210005655552 


196880302080 
183754948608 


131253534720 
131253534720 

The  draught  between  the  front  and  back  rollers  is  required 
from  the  following  particulars: — 

Front  rollers  traverse  307.625472  inches  a  minute. 
Back  rollers  traverse  23.9264256  inches  a  minute. 
23.9264256)307.625472(12.857  draught  between  the  front 
239264256  and  back  rollers. 


683612160 
478528512 


2050836480 
1914114048 


1367224320 
1196321280 


1709030400 
1674849792 


34180608 


200 


SELF-ACTING  MULES. 


The  draught  between  the  front  and  back  rollers  is  required 
from  the  following  particulars  : — 

Draught  between  the  front  and  middle  rollers,  11.71875. 
Draught  between  the  middle  and  back  rollers,  1.09714. 

11.71875  draught  between  front  and  mid.  rols. 
1.09714  draught  between  middle  and  back  rols. 

4687500 
1171875 
8203125 
10546875 
11718750 


12.8571093750  draught  between  the  front  and  back 

rollers. 

The  draught  between  the  front  and  middle  rollers  is  required 
from  the  following  particulars  : — 
Wheel  on  front  rollers,  20  teeth. 
Crown-wheel,  108  teeth. 
Change-pinion,  24  teeth. 
Wheel  on  back  rollers,  50  teeth. 

Wheel  on  the  end  of  back  rollers,  working  a  stud-wheel  which 

drives  the  middle  rollers,  32  teeth. 
Wheel  on  middle  rollers,  25  teeth. 
Diameter  of  front  rollers,  1  inch  or  fths. 
Diameter  of  middle  rollers,  |  inch,  or  gths. 

DRIVING-WHEELS. 

20  teeth,  wheel  on  front  rollers. 
24  teeth,  change-pinion. 

480 

32  teeth,  wheel  on  the  end  of  back  rollers. 


960 
1440 


15360 

fths,  or  I  inch  diameter  of  middle  rollers. 


92160  divisor. 


:4 


SELF-ACTING  MULES. 


201 


DRIVEN-WHEELS. 

108  teeth,  crown  wheel. 

50  teeth,  wheel  on  back  rollers. 


5400 

25  teeth,  wheel  on  middle  rollers. 


27000 
10800 


135000 

|ths,  or  1  inch,  diameter  of  front  rols. 


1080000  dividend. 

92160)1080000(11.71875  draught  between  the  front  and 
02160  middle  rollers. 


158400 
92160 


662400 
645120 


172800 
92160 


806400 
737280 


691200 
645120 


460800 
460800 

The  draught  between  the  front  and  back  rollers  is  required 
from  the  following  particulars : — 

Wheel  on  front  rollers,  20  teeth. 
Crown-wheel,  108  teeth. 
Change-pinion,  24  teeth. 
Wheel  on  back  rollers,  50  teeth, 

14 


202  SELF-ACTING  MULES. 

Diameter  of  front  rollers,  1  inch,  or  §ths. 
Diameter  of  back  rollers,  |  inch,  or  {rths. 

DRIVING-WHEELS, 

20  teeth,  wheel  on  front  rollers. 
24  teeth,  change-pinion. 

480 

|ths,  or  I  inch,  diam.  of  back  rollers. 


3360  divisor. 

DRIVEN-WHEELS. 

108  teeth,  crown-wheel. 

50  teeth,  wheel  on  back  rollers. 


5400 

f  ths,  or  1  inch,  diameter  of  front  rollers. 


43200  dividend. 


3360)43200(12.8571  draught  between  the  front  and 
3360  back  rollers. 


9600 
6720 


28800 
26880 


19200 
16800 


24000 
23520 


4800 
3360 


1440 

Xi.  B. — By  examining  the  different  systems  of  working  draughts 
as  shown  in  the  last  examples,  it  will  he  found  that  they  all 
agree  with  each  other ;  therefore,  any  of  the  systems  may  he 
adopted. 


SELF-ACTING  MULES.  203 


The  speed  of  the  long  drawing-out  shaft  is  required  from  the 
following  particulars: — 

Revolutions  of  twist-shaft  a  minute,  272. 
Back  pinion  on  twist-shaft,  18  teeth. 
^  f  Back  intermediate  wheel,  42  teeth. 
\  Back  adjustable  intermediate  wheel,  70  teeth. 
Back  change-wheel  on  back  shaft  driving  front  rols.  50  teeth. 
Wheel  on  back  shaft,  19  teeth. 

Back  change-wheel  on  long  drawing-out  shaft,  61  teeth. 

272  revolutions  of  twist-shaft  a  minute. 
18  teeth,  back  pinion  on  twist-shaft. 

2176 
272 


4896 

19  teeth,  wheel  on  back  shaft. 


44064 
4896 


93024  dividend. 


50  teeth,  change-wheel  on  back  shaft,  for  driving  front  rols. 
61  teeth,  back  change-wheel  on  long  drawing-out  shaft. 

3050  divisor. 

3050)93024(30.499,  or  nearly  SOJ  revolutions  of  long 
9150  drawing-out  shaft  a  min. 


15240 
12200 


30400 
27450 


29500 
27450 


2050 

*  These  are  only  carrying  or  connecting-wheels;  consequently,  they  are  oiTiitted 
in  the  ■wrork. 


204 


SELF-ACTING  MULES. 


The  speed  of  the  drawing-out  scroll-shaft  is  required  from  the 
following  particulars: — 

Revolutions  of  long  drawing-out  shaft  a  minute,  30.5. 
Bevil-wheel  on  long  drawing-out  shaft,  24  teeth. 
Bevil-wheel  on  scroll-shaft,  48  teeth. 

30.5  revols.  of  long  drawing-out  shaft  a  min. 
24  teeth,  bevil-wheel  on  drawing-out  shaft. 


1220 
610 

Teeth  of  bev.]   

wl,  on  scroll-  >  48)732.0(15.25  revolutions  of  drawing-out  scroll- 
shaft,  J       48  shaft  a  minute. 


252 
240 


120 

96 


240 
240 

The  speed  of  the  dravfing-ont  scroll-shaft  is  required  from  the 
following  particulars: — 

llevolutions  of  twist-shaft  a  minute,  272. 
Back  pinion  on  twist-shaft,  18  teeth. 

Back  change-wheel  on  back  shaft,  for  driving  front  rollers,  50 
teeth. 

Wheel  on  back  shaft,  19  teeth. 

Back  change-wheel  on  long  drawing-out  shaft,  61  teeth, 
Bevil-wheel  on  long  drawing-out  shaft,  24  teeth. 
Wheel  on  drawing-out  scroll-shaft,  48  teeth. 


SELF-ACTING  MULES. 


205 


272  revolutions  of  twist-shaft  a  minute. 
18  teeth,  back  pinion  on  twist-shaft. 


21V6 
272 


4896 

19  teeth,  wheel  on  back  shaft. 


44064 
4896 


93024 

24  teeth,  bevil- wheel  on  long  drawing-out  shaft. 


372096 
186048 


2232576  dividend. 

50  teeth,  back  change-whl.  on  back  shaft,  for  driv.  front  rols. 
61  teeth,  back  change-wheel  on  long  drawing-out  shaft. 


3050 

48  teeth,  bevil-wheel  on  drawing-out  scroll-shaft. 


24400 
12200 


146400  divisor. 

146400)2232576(15.25,  or  15|-  revolutions  nearly, 
146400  drawing-out  scroll  a  min. 

7685'i6 
732000 


365760 
292800 


729600 

732000— nearly. 


206 


SELF-ACTING  MULES. 


If  the  drawing-out  scroll  be  6|  inches  diameter,  making  15|- 
revolutions  a  minute  ;  how  many  inches  will  the  scroll,  or  carriage 
traverse  ? 

15.25,  or  15J  revolutions  of  scroll  a  minute. 
6.75,  or  6|  inches,  diameter  of  scroll. 


7625 
10675 
9150 


102.9375 

3.1416  circumference  when  the  diameter  is  1. 


6176250 
1029375 
4117500 
1029375 
3088125 


323.38845000,  or  nearly  323/^  inches,  drawing-out 

scroll  traverses  a  minute. 

The  length  delivered  by  the  front  rollers  a  stretch  is  required 
from  the  following  particulars : — 

Carriage,  or  drawing-out  scroll  traverses  323.38845  inches  a 
minute. 

Front  rollers  traverse  307.625472  inches  a  minute. 
Length  of  stretch  put  up,  60.5,  or  60|  inches. 

307.625472  inches  front  rollers  traverse  a  min. 
60.5,  or  60J  inches  length  of  stretch. 


1538127360 
18457528320 


18611.3410560  dividend. 


SELF-ACTING  MULES. 


207 


Car.  travs.  a  min.  323.38845  in.)18611.3410560(57.551  in.,  front 

161694225  rollers  deliver  a 
 stretch. 

244191855 

226371915 


178199406 
161694225 


165051810 
161694225 


33575850 
32338845 


1237005 

If  the  length  delivered  at  the  front  rollers  a  stretch,  be  57.551 
inches,  and  the  length  of  the  stretch  put  up,  be  60.5,  or  60|^ 
inches;  how  many  inches  a  stretch  does  the  carriage  gain? 

60.500,  or  60|-  inches,  length  of  stretch  put  up. 

57.551  inches,  length  deliv.  at  front  rols.  a  stretch. 

2.949,  or  nearly  3  inches  gain  of  carriage. 

The  draught  between  the  carriage  and  front  rollers  is  required 
from  the  following  particulars: — 

Carriage  traverses  323.38845  inches  a  minute. 
Front  rollers  traverse  307.625472  inches  a  minute. 
307.625472)323.388450(1.05124  draught  between  carriage 
307625472  and  front  rollers. 


1576297800 
1538127360 


381704400 
307625472 


740789280 
615250944 


1255383360 
1230501888 


24881472 


208 


SELF-ACTING  MULES. 


The  length  of  the  stretch  is  required  from  the  following  par- 
ticulars : — 

Front  rollers  deliver  57.551  inches  a  minute. 
Draught  between  carriage  and  front  rollers,  1.05124. 
57.551  inches,  front  rollers  deliver  a  minute. 
1.05124  draught  between  carriage  and  front  rollers. 

230204 
115102 
57551 
287755 
576510 


60.49991324,  or  60i  inches,  length  of  stretch. 

The  total  draught  at  mules  is  required  from  the  following 
particulars : — 

Draught  between  front  and  back  rollers,  12.857109375. 
Draught  between  carriage  and  front  rollers,  1.05124. 

12.857109375  draught  between  front  and  back  rols. 
1.05124  draught  between  car.  and  front  rols. 

51428437500 
25714218750 
12857109375 
64285546875 
128571093750 


13.51590765937500,  or  rather  more  than  13|  total  draught 
at  mules. 

The  total  draught  at  mules  is  required  from  the  following  par- 
ticulars : — 

» 

Revolutions  of  drawing-out  scroll  a  minute,  15.25, 
Revolutions  of  back  rollers  a  minute,  8.704. 
Diameter  of  scroll,  6f  inches,  or  54-8ths. 
Diameter  of  back  rollers,  |  inches,  or  7-8ths. 

15.25  revolutions  of  drawing-out  scroll  a  min. 
54-8ths,  or  6|  inches,  diameter  of  drawing- 

  out  scroll. 

6100 
7625 


823.50  dividend. 


SELF-ACTING  MULES. 


209 


8.704  revolutions  of  back  rollers  a  minute. 
7-8ths,  or  I  inch,  diameter  of  back  rollers. 

60.928  divisor. 

Divisor.  Dividend. 

60.228)823.500(13.515  total  draught  at  mules. 
60928 


214220 
182784 


314360 

304640 


97200 
60928 


362720 
304640 


58080 

The  total  draught  at  mules  is  required  from  the  following  par- 
ticulars : — 

Bevil-wheel  on  drawing-out  scroll-shaft,  48  teeth. 
*Bevil-wheel  on  long  drawing-out  shaft,  24  teeth. 

Back  change- wheel  on  drawing-out  shaft,  61  teeth. 

Wheel  on  back  shaft,  19  teeth. 

Wheel  on  front  rollers,  20  teeth. 

Crown-wheel,  108  teeth. 
*Change-pinion,  24  teeth. 

Wheel  on  back  rollers,  50  teeth. 

Diameter  of  drawing-out  scroll,  6f  inches,  or  54-8ths. 
Diameter  of  back  rollers,  |  inch,  or  7-8ths. 

*  These  wheels  are  omitted  in  working,  one  beint;  a  driving  and  the  other  a 
driveii-wheel,  each  containing  the  same  number  of  teeth. 


■ 


SELF-ACTING  MULES. 


DRIVING-WHEELS. 

48  teeth,  bevil-wheel  on  drawing-out  scroll-shaft. 
61  teeth  back  change-wheel  on  drawing-out  shaft. 

48 
288 


2928 

20  teeth,  wheel  on  front  rollers. 


58560 

7-8ths  inch,  diameter  of  back  rollers. 


409920  divisor. 

DRIVEN-WHEELS. 

19  teeth,  wheel  on  back  shaft. 
108  teeth,  crown-wheel. 

152 
190 


2052 

50  teeth,  wheel  on  back  rollers. 


102600 

54-8ths,  or  6|-  in.  diam.of  drawing-out  scroll. 


410400 
513000 


5540400  dividend. 

409920)5540400(13.5158  total  draught  at  mules. 
409920 


1441200 
1229760 

  2380800 

2114400  2049600 

2049600   

  3312000 

648000  3279360 

409920   

  32640 


SELF-ACTING  MULES, 


211 


iV,  B. — By  changing  the  50  teeth  wheel  on  the  hack  shaft,  it  loill 
affect  the  front  rollers  and  drawing-out  scroll  in  the  same 
2yroportion ;  consequently,  the  gain,  or  draught  at  carriage,  will 
remain  the  same.  The  gain,  or  draught  at  carriage,  may  be 
altered  by  changing  the  61  teeth  wheel  on  the  long  drawing- 
out  shaft;  both  being  driven-ioheels  from  the  first  moving  power, 
a  less  number  of  teeth  will  increase  the  speed,  whereas,  had 
they  been  driving-wheels,  it  loould  have  required  a  greater 
number  of  teeth  to  have  produced  an  increase  of  speed,  and  the 
reverse  for  a  decrease  in  speed. 

The  speed  of  the  quadrant-shaft  is  required  from  the  following 
particulars: — 

Revolutions  of  drawing-out  scroll  a  minute,  15.25. 

Diameter  of  scroll,  6.75  inches. 

Diameter  of  drum  on  quadrant-shaft,  6.125. 

15.25  revols.  of  drawing-out  scroll  a  minute. 
»  6.75,  or  6|  inches,  diameter  of  scroll. 


7625 
10675 
9150 

102.9375 

Diam.  of  drum  on  quad. -shaft,  6.125  in. )i02. 9375(16. 806  revols. 

6125       of  quad. -shaft 


a  rnin. 


41687 
36750 

49375 
49000 

37500 
36750 


750 

JSf.  B. — The  quadrant-shaft  is  driven  by  the  draiving-out  scroll 
band  while  the  carriage  is  drawing  out,  and  the  chain  on  the 
winding-on  drum  is  counterbalanced  by  a  lueight  at  the  eiid  of 
a  band  working  on  pulleys  and  connected  with  the  winding-on 


212 


SELF-ACTING  MULES. 


drum,  tvhich  is  out  of  geer  while  drawing  out,  and  is  put  into 
geer  hy  a  spring  connected  with  the  long  lever  and  vertical 
shaft  when  the  carriage  is  going  in;  during  which  time,  the 
speed  of  the  winding-on  drum  is  governed  by  a  strap  working 
the  governor-wheels  connected  with  the  worm,  when  the  slide 
to  which  the  winding-on  chain  is  affixed  rises  in  the  recess  of 
the  quadrant  hy  means  of  the  worm,  and  decreases  the  length 
of  the  chain  from  the  drum,  regulating  the  winding  on  accord- 
ing to  the  increasing  thickness  of  the  cop.  When  the  cop  has 
attained  the  intended  tltickiiess,  then  the  governor-wheels  cease 
to  tvork,  and  the  length  of  the  chain  going  on  the  winding-on 
drum  remains  the  same  till  the  cop  is  completed. 

The  number  of  teeth  the  quadrant  moves  a  stretch  is  required 
from  the  following  particulars  : — 

Carriage  traverses  323.38845  inches  a  minute.- 
Revolutions  of  quadrant-shaft  a  minute,  16.806. 
Wheel  on  quadrant-shaft,  22  teeth. 
Length  of  stretch,  60J  inches. 

16.806  revols.  of  quad. -shaft  a  min. 
22  teeth,  wheel  on  quad. -shaft. 


33612 
33612 


369.732 

60.5,  or  60|  in.,  length  of  stretch. 


1848660 
22183920 

Car.  travs.,  323.38845  in.)22368.7860(69.17  num.  of  teeth  quad. 

194033070  moves  a  stretch  of 

 Q^h  inches. 

296547900 
291049605 


54982950 
32338845 


226441050 
226371915 


69135 


SELF-ACTING  MULES.  \'^/^213''  - 

The  turns  an  inch  of  yarn  are  required  from  the  following: 
particulars  : — 

Bell-wheel  worked  by  a  worm  on  the  twist-shaft,  56  teeth. 

Diameter  of  the  grooved  pulley  on  the  twist-shaft,  17f  inches. 
/Diameter  of  grooved  twist-pulley,  driving  vertical  shaft,  lOJ 
V  inches. 

*  (Diameter  of  grooved  pulley  on  the  vertical  shaft,  lOJ  inches. 
/Diameter  of  grooved  pulley  on  tin  drums,  10  inches. 
\Diameter  of  tin  drums,  driving  the  spindles,  10  inches. 

Diameter  of  wharves  on  the  spindles,  |  inch. 

Length  of  stretch  put  up,  60^  inches. 

17.375,  or  17f  inches,  diam.  of  grooved  pul.  on 
66  teeth,  bell-wheel.  [the  twist-shaft. 


104250 
86875 


973.000  dividend. 

.875,  or  |ths  of  an  inch,  diam.  of  wharves. 
60.5,  or  60J  inches,  length  of  stretch. 


4375 
62500 


52.9375  divisor. 

52.9375)973.0000(18.38  turns  an  inch  of  yarn 
529375  required. 


4436250 
4235000 


2012500 
1588125 


4243750 
4235000 


8750 


^  *  These  are  all  omitted  in  the  work,  being  driving  and  driven,  of  the  snme 
dimensions. 


214 


SELF-ACTING  MULES. 


The  number  of  teeth  in  the  bell-wheel  is  required  from  the 
following  particulars : — 

Number  of  turns  an  inch  of  yarn  required,  18.38. 

Length  of  stretch  put  up,  60.5  inches. 

Diameter  of  wharves  on  the  spindles,  |  inch, 
f  Diameter  of  drum  driving  wharves,  10  inches. 
^  J  Diameter  of  pulley  on  drum  driving  wharves,  10  inches, 
j  Diameter  of  pulley  on  vertical  shaft,  10^  inches. 
(^Diameter  of  pulley  driving  vertical  shaft,  10^  inches. 

Diameter  of  pulley  on  twist-shaft,  17f  inches. 

18.38  turns  an  inch, 
60.5  inches,  length  of  stretch. 


9190 
110280 


1111.990,  or  1112  turns  in  a  st'ch  of  601  in. 
.875,  or  I  inch,  diam.  of  spindle  wharves. 

555995 
778393 
889592 

In.  diam.^  

of  pul.  on  y  17.375)972.99125(56  nearly,  number  of  teeth  re- 
tAvist-s'ft,  j  86875  quired  in  the  bell-wheel. 

104241 

104260— nearly. 

iV.  B. — All  the  rules  are  fully  laid  doivn  in  a  former  fart  of 
this  u'ork.    (See  Hand  Mules.) 

The  speed  of  the  short  going-in  shaft  is  required  from  the  fol- 
lowing particulars  : — 

Revolutions  of  twist-shaft  a  minute,  272. 
Wheel  on  loose  pulley,  36  teeth. 
Wheel  on  short  going-in  shaft,  54  teeth. 

•  These  are  omitted  in  the  work  on  account  of  being  driving  and  driven  of  the 
same  dimensions;  bnt  if  tlie  diameters  had  been  of  different  dimensions,  they  must 
have  been  made  use  of  as  in  former  examples. 


SELF-ACTING  MULES. 


215 


272  revolutions  of  twist-shaft  a  minute. 
36  teeth,  wheel  on  loose  pulley. 

1632 
816 

Teeth  of  wheel  ^   

on  short  going-in  V  54)9792(181.33,  or  ISIJ  revolutions  of  short 
shaft,  j       54  going-in  shaft  a  minute. 

439 
432 


72 
54 


180 
162 


180 
162 


18 

The  speed  of  the  long  going-in  shaft  is  required  from  the 
following  particulars: — 

Revolutions  of  twist-shaft  a  minute,  272. 
Wheel  on  loose  pulley,  36  teeth. 
Wheel  on  short  going-in  shaft,  54  teeth. 
Wheel  on  short  going-in  shaft,  17  teeth. 
Wheel  on  long  going-in  shaft,  20  teeth. 

272  revolutions  of  twist-shaft  a  minute. 
36  teeth,  wheel  on  loose  pulley. 


1632 
816 


9792 

17  teeth,  wheel  on  short  going-in  shaft. 


68544 
9792 


166464  dividend. 


216 


SELF-ACTING  MULES. 


54  teeth,  wheel  on  short  going-in  shaft. 
20  teeth,  wheel  on  long  going-in  shaft. 

1080  divisor. 

1080)166464(154.133  revolutions  of  long  going-in 
1080  shaft  a  minute. 


6846 
5400 


4464 
4320 


1440 
1080 


3600 
3240 


3600 
3240 


360 

The  speed  of  the  going-in  scroll-shaft  is  required  from  the 
following  particulars: — 

Revolutions  of  twist-shaft  a  minute,  272. 
Wheel  on  loose  pulley,  36  teeth. 
Wheel  on  short  going-in  shaft,  54  teeth. 
Wheel  on  short  going-in  shaft,  17  teeth. 
Wheel  on  long  going-in  shaft,  20  teeth. 
Bevil-wheel  on  long  going-in  shaft,  16  teeth. 
Bevil-wheel  on  scroll-shaft,  45  teeth. 

272  revolutions  of  twist-shaft  a  minute. 
36  teeth,  wheel  on  loose  pulley. 


1632 
816 

9792 


SELF-ACTING  MULES.  217 

9792 

17  teeth,  wlieel  on  short  going-in  shaft. 


68544 
9792 

166464 

16  teeth,  bevil-wheel  on  long  going-in  shaft. 


998784 
166464 


2663424  dividend. 

54  teeth,  wheel  on  short  going-in  shaft. 
20  teeth,  wheel  on  long  going-in  shaft. 


1080 

45  teeth,  bevil-wheel  on  scroll-shaft. 


5400 
4320 

48600  divisor. 

48600)2663424(54.80296  revolutions  of  going-in 
243000  scroll  a  minute. 


230424 
194400 


390240 
388800 


144000 
97200 


468000 
437400 


306000 
291600 


14400 


218 


SELF-ACTING  MULES. 


The  revolutions  of  the  going-in  scroll  a  stretch,  are  required 
from  the  following  particulars: — 

Circumference,  or  chase  of  scroll  a  stretch,  22  inches. 
Length  of  stretch  put  up,  60J  inches. 

22)60.5(2.75,  or  2f  revolutions  of  going-in 
44  scroll  a  stretch. 

165 
154 


110 
110 


The  speed  of  the  backing-off  wheel  is  required  from  the  fol- 
lowing particulars: — 

Revolutions  of  long  going-in  shaft  a  minute,  154.133. 
Wheel  on  long  going-in  shaft,  12  teeth. 
Backing-off  wheel,  77  teeth. 

154.133  revols.  of  long  going-in  shaft  a  min. 
12  teeth,  wheel  on  long  going-in  shaft. 


Teethofback-K^.jg^g  gQQ,24.02  revols.  of  backing-off  wheel 
mg-off  wheel,  ;  a  minute. 


809 
308 


160 
154 


6 


iV.  B. — The  haeJcmg-off  loheel  can  he  regulated  by  the  leather  fric- 
tion pulley ,  which  works  into  the  hacJcing-off  wheel,  and  may 
he  made  slacker,  or  tighter,  by  means  of  a  bolt  and  nut  con- 
nected with  the  friction  pulley.  The  proper  friction  on  the 
hacking-off  tvheel  is  very  essential,  which  will  soon  he  ascer- 
tained by  any  practical  person. 

Required,  from  the  following  particulars,  the  length  of  time  a 
stretch  the  carriage  occupies  while  going  in. 


SELF-ACTING  MULES.  219 

Eevolutions  of  going-in  scroll  a  minute,  54.80296. 
Revolutions  of  going-in  scroll  a  stretch,  2.75. 

2.75  revols.  of  going-in  scroll  a 
60  seconds,  1  min.  [stretch. 

Revols.  of  going-inK^  gQ29exig5_QQQQQ,3  010-^86,  or  rather 
scroll  a  minute,      J  K-i  inooo  ^v, 

'      ^  16440888  more  than 

  3  seconds 

5911200  a  stretch. 

5480296 


43090400 
38362072 


47283280 
43842368 


34409120 
32881776 


1527344. 

If  it  requires  56  turns  or  revolutions  of  the  twist-shaft  to  draw 
out  one  stretch,  what  time  will  it  require,  if  the  twist-shaft  makes 
272  turns  or  revolutions  a  minute  ? 

272)56.0(.20588  minute  a  stretch. 

544 


1600 
1360 


2400 
2176 


2240 
2176 

64 

.20588  minute  a  stretch. 

60  seconds,  1  minute. 


12.35280  seconds  required  to  draw  out  1 

stretch. 


220 


SELF-ACTING  MULES. 


The  number  of  stretches  a  mule  a  minute  is  required  from 
the  following  particulars,  allowing  2J  seconds  a  stretch  for 
backing  olF. 

Drawing  out  a  stretch,  12.3528  seconds. 
Backing  off  a  stretch,  2.5  seconds. 
Going  in  a  stretch,         3.0107  seconds. 

17.8635  seconds  a  stretch. 

17.8635)60.0000(3.3588,  or  rather  more  than  stretches 
535905  a  minute,  each  mule. 


640950 
535905 


1050450 
893175 


1572750 
1429080 


1436700 
1429080 


7620 

If  a  mule  produce  3.3588  stretches  a  minute,  and  each  stretch 
be  60  inches,  how  many  hanks  a  spindle  will  be  produced  in  one 
week,  allowing  them  to  work  successively  for  65  hours  ? 

3.3588  stretches  a  minute. 
60  minutes,  1  hour. 

201.5280  stretches  an  hour. 
65  hours  in  1  week. 


1007640 
1209168 


13099.320  stretches  in  1  week. 
60  inches  each  stretch. 


785959.200  inches  of  yarn  a  spindle  a  week. 


A 


SELF-ACTING  MULES.  221 


1  yard  jg)  inches  of  yarn  a  spindle  a  week. 

36mclies,jg^-^gQC)g3  2 

21832.2  yards  a  spindle  a  week. 


1  hank  is  840  yds.)21832.2(25.99  nearly  26  hanks  a  spindle  a, 
1680  week.. 


5032 
4200 

8322 
7560 

7620 
7560 

60 

The  speed  of  the  leather-contact  pulley  is  required  from  the 
following  particulars : — 

Revolutions  of  twist-shaft  a  minute,  272. 

Wheel  on  loose  pulley,  36  teeth. 

Wheel  on  leather-contact  pulley  shaft,  33  teeth. 

272  revolutions  of  twist-pulley  a  min. 
36  teeth,  wheel  on  loose  pulley. 


1632 
816 

Teeth-wheel  on  'J   • 

leather-contact  133)9792(296.727  revols.  of  leather-contact 
pulley,  j      66  pulley  a  minute. 

319 
297 

222  90 
198  66 

240  240 
231  231 

90  9 


222 


SELF-ACTING  MULES. 


If  the  leather-contact  pulley  be  3J  inches  diameter,  making 
296.727  revolutions  a  minute,  what  will  it  traverse  ? 

296.727  revols.  of  leather-contact  pulley  a  min. 
3.75,  or  3|  inches,  diameter  of  do. 


1483635 
2077089 
890181 


1112.72625 

3.1416  circumference  when  the  diameter  is  1. 


667635750 
111272625 
445090500 
111272625 
333817875 


3495.740787000  inches  leather-contact  pulley  traverses 

a  minute. 

The  revolutions  of  the  spindles  for  the  twist-shaft  once  are  re- 
ijuired  from  the  following  particulars : — 

Revolutions  of  spindles  a  stretch,  1112. 
Revolutions  of  twist-shaft  a  stretch,  56, 

Revols.  of  twist-shaft^  8)1112  revols.  of  spindles  a  stretch. 

a  stretch  is  56,  then  >  

8  X  7=56,  J  7)139 

19.857  revols.  of  the  spindles  for  the 
twist-shaft  once. 

Required,  from  the  following  particulars,  the  revolutions  a 
stretch  of  the  spindles  for  winding  on  yarn  at  the  beginning  of 
the  set — i.  e.,  when  the  spindles  are  bare : — 

Diameter  of  winding-on  drum,  4|-  or  4.125  inches. 
Length  of  chain  thrown  off  drum,  60J  or  60.5  inches. 
Wheel  on  the  winding-on  drum,  41  teeth. 
Pinion  on  winding-on  drum-shaft,  25  teeth. 


SELF-ACTING  MULES. 


223 


f  Bevil-wheel  on  winding-on  drum-shaft,  40  teeth. 
\  Bevil-wheel  on  foot  of  vertical  shaft,  40  teeth. 
Diameter  of  pulley  on  vertical  shaft,  10^  or  10.25  inches. 
Diameter  of  spindle-wharves,  ^  or  .875  inch. 

4.125  inches,  diameter  of  winding-on  drum, 
3.1416  inches,  circum.  when  the  diam.  is  1. 


24750 
4125 

16500 

4125 
12375 


12.9591000 

25  teeth,  pinion  on  winding-on  drum-shaft. 


647955 
259182 


323.9775 

.875  inches,  diameter  of  wharves. 


16198875 
22678425 
25918200 


283.4803125  divisor. 

60.5  in.,  length  of  chn.  thrown  off  wind. -on  drum. 
41  teeth,  wheel  on  winding-on  drum. 


605 
2420 


2480.5 

10.25  inches  diam.  of  pulley  on  vertical  shaft. 


124025 
49610 
248050 


25425.1250000 

*  These  are  omitted  in  the  work,  being  driving  and  driven;  and  the  tin  drums 
for  driving  spindles  are  omitted,  being  intermediate. 


\ 


224 


SELF-ACTING  MULES. 


283.4803125)25425.1250000(89.689 
22678425000 


27467000000 
25513228125 


19537718750 
17008818750 


25289000000 
22678425000 


26105750000 
25513228125 


592521875 

If  it  requires  the  bare  or  empty  spindles  to  make  89.689  re- 
volutions to  wind  on  a  stretch  60 J  inches  long;  what  will  the 
circumference  and  diameter  of  the  spindles  be  ? 

89.689)60.5000(.67455  inch,  circumference  of  spindles. 
538134 


668660 
627823 


408370 
358756 


496140 
448445 


476950 
448445 


revols.  of  spindle  a  stretch, 
winding  yarn  on  bare  spin- 
dles. 


28505 


62832 


46280 
31416 


148140 
125664 


224760 
219912 


4848 


The  speed  of  the  spindles  for  winding  on  the  yarn  will  be  in 
accordance  with  their  diameter,  from  which  may  be  ascertained 
the  size  of  the  winding-on  drum,  or  pinion  on  the  winding-on 
drum-shaft. 

If  the  diameter  of  the  spindles  be  ^  inch;  how  many  revolu- 
tions must  they  make  to  wind  on  605-  inches  of  yarn? 


3.1416  circumference  when  the  diameter  is  1. 
.25,  or  ^  inch,  diameter  of  spindles. 


157080 
62832 


.785400  circumference  of  spindle. 

.7854)60.5000(77  revolutions  required  for  spin- 
54978         die,  to  wind  on  60J  inches  of 


Required,  the  revolutions  of  the  winding-on  drum,  for  the 
spindles  to  make  77  revolutions,  or  turns  a  stretch,  according  to 
the  following  particulars : — 

Diameter  of  spindle  wharves,  |,  or  .875  inch. 
Diameter  of  pulley  on  vertical  shaft,  lOj  inches. 


yarn. 


55220 
54978 


242 


226  SELF-ACTING  MULES. 

Pinion  on  winding-on  drum-shaft,  25  teeth. 
Wheel  on  winding-on  drum,  41  teeth. 

.875  diameter  of  spindle-wharves. 
77  revols.,  or  turns  of  spindles  a  stretch. 


6125 
6125 


67.375 

25  teeth,  pinion  on  winding-on  drum-shaft. 


336875 
134750 


1684.375  dividend. 

10.25  inches,  diameter  of  pulley  on  vertical  shaft. 
41  teeth,  wheel  on  winding-on  drum. 

1025 
4100 


420.25  divisor. 

420.25)1684.375(4  revolutions  of  winding-on  drum 
168100       a  stretch  required. 

337 

If  the  winding-on  drum  be  required  to  make  4  revolutions  a 
stretch;  what  must  the  circumference  be  to  wind  on  60 J  inches 
of  chain  ? 

4)60.5 


15.125,  or  15J  inches,  circumference  of  drum. 

If  the  winding-on  drum  be  15.125,  or  15J  inches  circumfer- 
ence; what  will  the  diameter  be? 


SELF-ACTINa  MULES. 


227 


3.1416)15.1250(4.8144  inches,  diameter  of  winding- 
125664  on  drum. 


255860 
251328 


45320 
31416 


139040 
125664 


133760 
125664 


8096 

The  iron-contact  pulley  on  the  cam-shaft  is  SjJ  inches  diame- 
ter, and  has  4  recesses,  or  spaces  in  it  at  an  equal  distance,  which 
relieve  it  from  the  leather-contact  pulley,  and  is  also  assisted  by 
4  pins  in  the  front  of  the  escape-plate,  each  of  which  works 
against  a  spring,  when  the  spring  at  the  back  of  the  escape-plate 
moves  from  one  bolster  to  another  when  acted  upon  by  the  lever 
connected,  and  which  gives  power,  by  the  assistance  of  the  leather- 
contact  pulley,  to  the  different  motions  on  the  cam-shaft,  which  is 
as  follows : — 

Motions  from  the  escape-plate. 

First — Back  and  front  cams  for  the  strap-lever. 

Second — Backing-off  cam  connected  with  the  friction-pulley, 

working  into  backing-off  wheel-pulley. 
Third — Front  roller  eccentric. 

Fourth — Stop-finger  connected  with  the  bell-wheel-shaft. 
Fifth — Going-in  eccentric. 
Sixth — Drawing-out  eccentric. 

The  following  are  the  alternate  movements  on  the  cam-shaft 
each  stretch : — 

First — Roller  geer  and  drawing-out  motions. 
Second — Twist  motion. 
Third — Backing-off  motion. 
Fourth — Going-in  motion. 


228 


SELF-ACTINa  MULES. 


THE  FOLLOWING  ARE  THE  PARTICULARS  OF  THE  SELF-ACTING 

MULES: — 

Revolutions  of  twist-shaft  a  minute,  272. 
Revolutions  of  spindles  a  minute,  5401.1428. 
Revolutions  of  vertical  shaft  a  minute,  461.07317. 
Revolutions  of  front  rollers  a  minute,  97.92. 
Revolutions  of  middle  rollers  a  minute,  11.14112. 
Revolutions  of  back  rollers  a  minute,  8.704. 
Revolutions  of  long  drawing-out  shaft  a  minute,  30.499  or  30J. 
Revolutions  of  drawing-out  scroll  a  minute,  15.249  or  15J. 
Revolutions  of  quadrant-shaft  a  minute,  16.806. 
Revolutions  of  short  going-in  shaft  a  minute,  181.333. 
Revolutions  of  long  going-in  shaft  a  minute,  154.1333. 
Revolutions  of  going-in  scroll  a  minute,  54.80296. 
Revolutions  of  going-in  scroll  a  stretch,  2.75  or  2f . 
Revolutions  of  backing-off  wheel  a  minute,  24.02. 
Revolutions  of  leather-contact  pulley  a  minute,  296.727. 
Revolutions  of  spindles  per  twist-shaft  once,  19.857. 
Revolutions  of  bare  or  empty  spindles  for  winding  on  yarn  a 

stretch,  at  the  beginning  of  set,  89.689. 
Diameter  of  pulleys  on  twist- shaft,  12  inches. 
Diameter  of  grooved  band-pulley  on  twist-shaft,  17f,  8,  and 

18|  inches. 

Diameter  of  grooved  twist-pulley  for  driving  vertical  shaft,  lOJ 
inches. 

Diameter  of  grooved  pulley  on  vertical  shaft,  lOj  inches. 
Diameter  of  grooved  pulley  on  tin  drums,  10  inches. 
Diameter  of  tin  drums  for  driving  spindles,  10  inches. 
Diameter  of  spindle-wharves,  |  inch. 
Diameter  of  front  rollers,  1  inch. 
Diameter  of  middle  rollers,  f  inch. 
Diameter  of  back  rollers,  |  inch. 
Diameter  of  drawing-out  scroll,  6f  inches. 
Diameter  of  quadrant-shaft  drum,  6^  inches. 
Diameter  of  leather-contact  pulley,  3f  inches. 
Diameter  of  iron-contact  pulley,  5}^  inches. 
Diameter  of  winding-on  drum,  4^  inches. 
Diameter  of  spindles,  .2147  inch. 
Front  rollers  traverse  a  minute,  307.625472  inches. 
Middle  rollers  traverse  a  minute,  26.250707  inches. 
Back  rollers  traverse  a  minute,  23.926425  inches. 
Drawing-out  scroll  traverses  a  minute,  323.38845  inches. 


SELF-ACTING  MULES. 


229 


Front  rollers  traverse  a  stretch,  57.551  inches. 
Carriage  traverses  a  stretch,  60.5  inches. 
Going-in  scroll  traverses  a  revolution,  22  inches. 
Leather-contact  pulley  traverses  a  minute,  3495.749787  inches. 
Draught  between  the  middle  and  back  rollers,  1.0971428,  nearly 

Draught  between  the  front  and  middle  rollers,  11.71875. 

Draught  between  the  front  and  back  rollers,  12.8571. 

Draught  between  the  front  rollers  and  carriage,  1.05124. 

Total  draught  at  the  mules,  13.5158. 

Gain  at  carriage  each  stretch,  2.949,  nearly  3  inches. 

Turns  each  inch  in  yarn,  18.38. 

Turns  each  stretch  of  60J  inches,  1112. 

Bell-wheel,  56  teeth. 

Number  of  teeth  the  quadrant  moves  each  stretch  of  60J  inches, 
69.17. 

Time  each  stretch  drawing  carriage  out,  12.3528  seconds. 

Time  each  stretch  allowed  for  backing  off,  2.5  seconds. 

Time  each  stretch  carriage  going  in,  3.0107  seconds. 

Time  required  to  complete  each  stretch,  17.8635  seconds. 

Number  of  stretches  a  minute,  each  mule,  3.3588. 

Number  of  stretches  an  hour,  each  mule,  201.528. 

Number  of  stretches  a  week,  each  mule,  13099.32. 

Number  of  hanks  a  spindle  a  week,  25.99,  or  26  hanks  nearly. 

The  faller  rises  by  the  lowering  of  the  coping-rail,  by  means 
of  a  lever  connected  with  the  faller-sector  working  upon  it.  The 
faller-sector  at  the  same  time  works  into  a  22  teeth-wheel  on 
the  faller-shaft. 

The  backing-off  eccentric  is  loose  on  the  vertical  shaft;  and 
the  chain  attached  to  the  eccentric  and  connected  with  the  faller- 
sector  is  governed  by  a  catch  fixed  to  the  plate  of  the  eccentric, 
working  against  the  ratchet-wheel  while  backing  oif. 

N.  B. —  Tlie  number  of  teeth  in  the  ratchet-ivheel  is  88. 

At  the  commencement  of  a  set,  when  the  spindles  are  bare  or 
empty,  great  care  must  be  taken  to  set  the  coping-rail  and  wind- 
ing-on  chain  to  their  proper  places,  by  means  of  the  worm  or 
screw  connected ;  for,  if  right,  then  they  will  regulate  them- 
selves afterwards. 

Whatever  bevil  the  coping-rail  may  have  will  be  the  length  of 
the  chase  given  to  the  faller,  which  may  be  increased  or  de- 
creased by  giving  more  bevil  to  the  coping-rail,  and  by  changing 
the  wheel  on  the  worm-shaft  connected  with  the  shaper  or  coping- 


is 


230 


HANK,  OR  PROPORTION  OF  HANK,  ETC. 


plate.  The  cop  may  be  made  larger  or  smaller.  A  larger  wheel 
■will  make  a  larger  cop,  on  account  of  the  worm-shaft  connected 
with  the  shaper  or  coping-plate  moving  slower ;  and  a  smaller 
wheel  will  make  a  smaller  cop  by  the  worm-shaft  connected  with 
the  shaper  or  coping-plate  moving  quicker,  there  being  a  finger 
attached  to  the  carriage  which  works  the  catch  on  the  wheel  of 
the  worm-shaft,  and  causes  the  wheel  to  move  one  tooth  each 
stretch,  which  gives  the  bevil  to  the  coping-rail. 

It  is  of  the  utmost  importance  that  every  attention  be  given 
to  machinery  by  having  every  part  of  the  machine  properly  ad- 
justed, and  set  square  with  the  scrolls  and  other  bands  of  a  pro- 
per tightness;  and  that  regular  cleaning  and  oiling  be  particu- 
larly attended  to,  which  is  indispensable  in  all  machinery — the 
neglect  of  which  causes  machinery  to  work  ill,  and  destroys  it 
much  sooner  than  it  otherwise  would  have  been  had  proper  care 
been  taken. 

Neglect  always  brings  the  best  machinery  into  disrepute,  con- 
sequently is  injurious  to  the  best  machinists,  and  trade  generally 
suffers  materially. 

I  ^Within  these  last  few  years,  there  have  been  a  number  of 
patents  obtained  by  different  machinists  for  improvements  in 
machinery,  used  in  all  the  different  operations  of  carding,  draw- 
ing, slabbing,  roving,  spinning,  and  weaving. 

HANK,  OR  PROPORTION  OF  HANK,  ETC.  IN  EACH  OPERATION. 

The  following  examples  will  show  the  hank  and  the  decimal, 
or  proportion  of  hank,  in  each  and  every  operation,  from  the 
spinning  to  the  lap  machine. 

Suppose  the  numbers  or  counts  of  yarn  be  40's,  with  a  draught 
of  9.6,  or  9 /q,  what  hank  roving  will  be  required  ? 

Draught,  9.6)40.0(4.1666,  or  4|  hank  roving  required. 
384 


160 
96 


640 
576 


640 
576 


640 

676 


640 


64 


HANK,  OR  PROPORTION  OP  HANK,  ETC. 


231 


If  the  draught  at  roving-frame  he  7.5,  or  7^,  producing  a  4^ 
hank  roving,  what  hank  -vvill  the  slabbing  be,  allowing  2  slabbings 
to  each  roving  ? 

iV.  B. —  Where  there  is  doubling,  multiply  the  hanh,  or  propor- 
tion of  hanh,  hy  the  number  of  ends  doubled,  and  divide  by 
the  draught. 

Hank  roving,  4J,  or  4.1666 

2,  number  of  ends  doubled. 

Draught  7J,  or  7.5)8.3333(1.1111,  or  1^  hank  slabbing. 
75 


83 
75 


83 
75 


83 
75 


83 
75 


8 

If  the  draught  at  the  slabbing-frame  be  6.875,  and  the  slab- 
bing be  1.1111,  or  1^  hank,  what  decimal  or  proportion  of  hank 
will  the  drawing  be,  put  up  at  the  back  of  slabbing-frame,  there 
being  no  doubling  ? 

Draught,  6.875)1.1111(0.1616  decimal,  or  proportion  of  hank, 
6875  last  head  of  drawing. 


42361 
41250 


11111 

6875 


42361 
41250 


1111 


232 


HANK,  OR  PROPORTION  OF  HANK,  ETC. 


If  8  ends  be  put  up  at  the  last  head  of  drawings,  and  the 
draught  be  6.125,  and  the  decimal  of  the  hank  0.1616;  what 
decimal,  or  proportion  of  hank  will  the  drawings  be  that  are  put 
up  ? 

0.1616  decimal,  or  proportion  of  hank  at 
8  ends  doubling.  [last  head. 

Draught,  6i,  or  6.125)1.2929(0.211  decimal,  or  proportion  of 
12250  hank  at  middle,  or  second 
  head  of  drawings. 

6792 

6125 


6679 
6125 


554 

If  the  hank  drawing  at  second  head  be  0.211;  what  will  the 
decimal,  or  proportion  of  hank  be  at  the  first  head,  if  the  draught 
be  6.25,  and  the  doubling  8? 

0.211  decimal,  or  proportion  of  hank  at 
8  ends  doubling.        [middle  head. 

Draught,  6|-,  or  6.25)1.688(0.27  decimal,  or  proportion  of 
1250  hank  at  first  head  of  draw- 

  ings. 

4880 
4875 


5 

If  the  decimal,  or  proportion  of  hank  at  the  first  head  of  draw- 
ings be  0.27,  the  draught  6.25,  and  the  doubling  8;  what  decimal, 
or  proportion  of  hank,  will  the  carding  be  ? 


HANK,  OR  PROPORTION  OF  HANK,  ETC. 


233 


0.27  decimal  of  hank  at  first  head  of 
8  ends  doubling.  [drawings. 


Draught,  6J,  or  6.25)2.1600(0.3456  decimal  of  hank  card- 
1875  ing. 

2850 
2500 


3500 
3125 

3750 
3750 


If  the  decimal  of  the  hank-carding  be  0.3456,  and  the  draught 
at  the  carding-engine  be  130;  what  will  the  decimal  of  the  hank 
lap  be? 

Dr't  at  carding-engine,  130)0.3456(.00265846  decimal,  or  pro- 

260  portion  of  hank 

lap. 


856 


760 
650 


1100 
1040 


600 
520 

800 
780 

20 

iV".  B. — The  weight  of  any  number  of  yards  of  carding  or  draw- 
ing may  he  found  in  the  tables,  according  to  the  decimal,  or 
proportion  of  hank. 
16 


234 


HANK,  OR  PROPORTION  OF  HANK,  ETC. 


If  the  decimal,  or  proportion  of  the  hank  lap  be  0.00265846, 
and  the  draught  at  the  lap  machine  be  2.75,  or  2| ;  what  -will 
the  decimal,  or  proportion  of  the  hank  of  cotton  fed  on  feed-cloth 
at  the  lap  machine  be  ? 

Draught  at  lap  machine,  2.75)0.00265846(0.0009667  decimal  of 

2475  hank  fed  on  feed- 

  cloth  at  lap  ma- 

1834  chine. 
1650 


1846 
1650 


1960 
1925 


35 

If  the  decimal,  or  proportion  of  hank  at  the  lap  machine  be 
0.0009667;  what  will  the  net  weight  of  cotton  fed  on  30  inches 
of  feed-cloth  at  the  lap  machine  be? 

Look  in  the  table  of  dividends  for  inches,  and  opposite  30  will 
be  found  6.9444  the  dividend;  which,  divided  by  0.0009667  the 
decimal,  or  proportion  of  hank  at  the  lap  machine,  will  give  the 
net  weight  of  cotton  in  grains. 

Decimal  of  hank,  0.0009667)6.9444(7183  grs.,  or  1  lb.,  0  oz.,  7 

67669         dwts.,  15  grains. 


17754 
9667 


80874 
77336 


35384 
29001 


6383 

B. —  The  above  weight  being  subtracted  from  the  gross  weight 
of  cotton  fed  on  feed-cloth  at  lap  machine,  will  give  the  weight 
of  loss  sustained  in  working. 


LOSS  IN  WORKING. 


235 


LOSS  IN  WORKING. 

Suppose  there  be  18-^-  ounces  of  cotton  fed  on  the  feed-cloth 
at  the  lap  machine,  and  the  weight  of  yarn  produced  (as  appears 
from  the  preceding  example)  be  1  ft.,  0  oz.,  7  dwts.,  and  15 
grains;  what  will  the  loss  sustained  in  working  be? 

oz.    dwts.  grs. 

18J  ounces,  =  18  .  .  9  .  .    2J  weight  of  cotton  at  lap  machine. 
16  .  .  7  .  .  15   weight  of  yarn  produced. 

2  .  .  1  .  .  llf  weight  lost  in  working. 
Or, 

The  loss  sustained  in  working  any  kind  of  cotton  maybe  found 
in  the  following  manner: — 

Multiply  all  the  draughts  together  successively  for  a  divisor, 
and  all  the  doublings  together  accordingly,  and  that  product  by 
the  numbers  of  yarn  produced  for  a  dividend,  and  the  quotient 
will  be  the  decimal,  or  proportion  of  the  hank. 

Then  look  for  the  dividend  in  the  table  opposite  the  number 
of  inches  any  given  weight  of  cotton  is  fed  on  the  feed-cloth  at 
the  lap  machine,  and  divide  by  the  decimal,  or  proportion  of  the 
hank,  and  the  quotient  will  be  the  net  weight  in  grains;  which, 
subtracted  from  the  weight  of  cotton  fed  on  the  feed-cloth  at  the 
lap  machine,  will  show  the  loss  sustained  in  working. 

The  loss  sustained  in  each  operation  may  be  ascertained  in  the 
same  manner. 

Suppose  the  draughts  and  doubling  are  as  follows :  the  num- 
bers to  be  spun  40's,  and  the  weight  of  cotton  fed  on  30  inches 
of  feed-cloth  at  the  lap  machine  be  18 J  ounces;  what  will  be  the 
loss  in  working  ? 

Draught  at  lap  machine,  2.75. 
Draught  at  carding-engine,  180. 
Draught  at  1st  head-drawing,  6.25. 
Draught  at  2d  head-drawing,  6.25. 
Draught  at  3d  head-drawing,  6.125. 
Draught  at  slabbing-frame,  6.875. 
Draught  at  roving-frame,  7.5. 
Draught  at  mules,  9.6. 


LOSS  IN  WORKING. 


Doubling  1st  head-drawing,  8. 
Doubling  2d  bead-drawing,  8. 
Doubling  3d  head-drawing,  8, 
Doubling  roving-frame,  2. 

DRAUGHTS. 

2.75  lap  machine. 
130  carding-engine. 


8250 
275 


357.60 

6J  draught  at  1st  head-drawing. 


2145.0 
89375 


2234.375 

6J  draught  at  2d  head-drawing. 


13406.250 

55859375 


13964.84375 

6|  draught  at  3d  head-drawing. 


83789.06250 
174560546875 

 [to  the  last  head  of  drawing! 

85534.66796875  total  draught  from  lap  machic 
6.875  draught  at  slabbing-frame. 


42767333984375 
59874267578125 
68427734375000 
51320800781250 


588050.84228515625 


LOSS  IN  WORKING.  237 

Draughts  )  588050.84228515625 

continued,  /  7.5  draught  at  roving-frame. 

294025421142578125 
411635589599609375 


4410381.317138671875 

9.6  draught  at  mules. 


26462287902832031250 
39693431854248046875 


Divisor  42339660.6445312500000  total  draughts. 

8  doubling  1st  head-drawing. 
8  doubling  2d  head-drawing. 


64 

8  doubling  3d  head-drawing. 


512 

2  doubling  roving-frame. 

1024  total  doublings. 
40's  number  spun^ 


Dividend  40960 

42339660.64453125)40960.000000000000(0.0009674  decimal, 
38105694580078125  or  proportion 

 of  hank  at  lap 

28543054199218750    '  machine. 
25403796386718750 


31392578125000000 
29637762451171875 


17548156738281250 
16935864257812500 


612292480468750 


238 


LOSS  IN  WORKING. 


The  dividend  for  30  inches  is  6.9444,  which,  divided  by 
0.0009674,  the  decimal  or  proportion  of  the  hank  at  the  lap 
machine,  will  give  the  weight  of  yarn  in  grains  produced,  which, 
subtracted  from  the  18f  ounces  of  cotton  fed  on  the  feed-cloth 
at  the  lap  machine,  will  show  the  loss  sustained  in  working. 

Dec.  or  prop,  of  hank,  0.0009674)6.9444(7178  grains  or  16  oz., 

67718         7  dwts.,  10  grs. 

  of  yarn  produced 

17264       from  18i  oz.  of 
9674  cotton. 


75904 
67718 


81864 
77392 


4472 

oz.     dwts.  grains. 

Cotton  consumed  at  lap  machine,  18  .  .  9  .  .  2| 
Yarns  produced,  16  .  .  7  .  .  10 

Loss  sustained  in  working,  2  .  .  1  .  .  16f 

The  weight  of  cotton  fed  on  any  given  length  of  feed-cloth  at 
the  lap  machine,  reduced  to  grains,  may  be  divided  by  the 
draughts,  and  multiplied  by  the  doublings  successively,  through 
each  operation,  which  will  show  the  gross  weight  in  grains  for 
the  same  length,  as  the  given  length  of  feed-cloth  at  the  lap 
machine,  which  may  be  extended  to  any  length,  the  weight  being 
in  proportion. 

The  net  weight  of  the  same  length,  according  to  the  hank  or 
proportion  of  hank  in  the  same  operation,  being  subtracted  from 
the  gross  weight,  will  show  the  loss  sustained  at  each  operation, 
or  the  whole  loss  throughout  the  different  processes  of  working. 

I^.  B. — Proceed  with  the  same  particulars  as  in  the  last  ex- 
amples. 

If  there  be  18|-  ounces  of  cotton  fed  on  30  inches  of  feed- 
cloth  at  the  lap  machine,  what  weight  should  the  same  length 


LOSS  IN  WORKING. 


239 


weigh  at  the  different  processes  (allowing  no  loss),  if  the  draughts 
and  doubling  be  as  follows  ? 

DRAUGHTS. 

Lap  machine,  2.75,  or  2f. 
Carding-engine,  130. 
1st  head  of  drawings,  6.25,  or  6J. 
2d  head  of  drawings,  6.25,  or  6J. 
3d  head  of  drawings,  6.125,  or  6J. 
Slabbing-frame,  6.875,  or  6|. 
Roving-frame,  7.5,  or  7|. 
Mules,  9.6,  or  9^%. 

DOUBLING. 

1st  head  of  drawings,  8. 
2d  head  of  drawings,  8. 
3d  head  of  drawings,  8. 
Roving-frame,  2. 

Reduce  18J  ounces  to  grains  for  the  dividend. 

437.5  grains=l  oz. 
18.5,  or  18J  ounces  of  cotton  fed 
  on  feed-cloth. 

21875 
35000 
4375 


Draught  at  lap  ma.  2.75)8093.75(2943.2  grs.,  or  6  oz.,  13  dwts. 

550  6-^  grs.,  weight  of  30 

  in.  of  lap, 

2593 
2475 


1187 
1100 


875 

825 


500 

550 — nearly. 


240 


LOSS  IN  WORKING. 


2943.2  grains,  weight  of  30  inches  of  lap  ;  draught  at  the  card- 
ing-engine  130. 

130)2943.2(22.64  grains,  weight  of  30  inches 
260  of  carding. 


343 
260 


832 
780 


520  . 
520 

22.64  grains,  weight  of  30  inches  of  carding ;  draught  at  the 
1st  head  of  drawings  6.25,  and  doubling  8. 

22.64  grains,  weight  of  carding. 

8  ends,  doubling  at  1st  head  of  draw- 

  ings. 

Draught,  6.25)181.12(28.9792  grains,  or  1  dwt.,  4.9792 
1250  grs.,  weight  of  30  inches 

  of  drawing  at  the  1st 

5612  head. 
5000 


6120 
5625 


4950 
4375 


5750 
5625 


1250 
1250 


LOSS  IN  WORKING. 


241 


28.9792  grs.,  weight  of  drawing  1st  head. 
8  ends  doubling. 
Draught  at  2d~|  

head  of  draw-  V  6.25)231.8336(37.093  grains,  or  1  dwt.,  13.093 
ings,  j  1875  grs.,  weight  of  30  inches 
  of  drawing  2d  head. 

4433 

4375 


5836 
5625 


2110 
1875 


235 


37.093  grains,  weight  of  30  inches  of  drawing  at  2d  head ; 
draught  at  3d  head  of  drawings  6.125,  and  doubling  8. 

37.093  grs.,  weight  of  30  inches  of  drawing. 
8  ends  doubling. 
Draught  at ")  

3d  head  of  V  6.125)296.746(48.448  grs.,  or  2  dwts.,  0.448  grs., 
drawing,  j  24500  weight  of  30  inches  of  draw- 
  ing  at  the  third  head. 

51746 

49000 


27460 
24500 


29600 
24500 


51000 
49000 


2000 


48.448  grains,  weight  of  30  inches  of  drawing  at  3d  or  last  head; 
draught  at  slabbing-frame  6.875  (no  doubling). 


242 


LOSS  IN  WORKING, 


Draught  at  slabbing-frame,  6.875)48.448(7.04698  grains,  weight 


of  slabbing. 


82300 
27500 


48000 
41250 


67500 
61875 


56250 
55000 


1250 


7.04698  grs.,  weight  of  30  in.  of  slabbing. 
2  ends  doubling  at  roving-frame. 


7.5)14.09396(1.88  grains,  weight  of  30  inches 


659 
600 


593 

600 — nearly. 


1.88  grains,  weight  of  30  inches  of  roving ;  draught  at  mules 
9.6  (no  doubling). 

Draught  at  mules,  9.6)1.88(0.195833  decimal  of  a  grain,  weight 


48125 


of  30  inches 


of  roving. 


96 


of  30  inches  of  yarn. 


920 
864 


560 
480 


320 
288 


800 
768 


320 
288 


320 


32 


144,  the  number  of  30'iriche's  in  l'' 


lea,  or  120  yards. 


783333 
783333 
195833 


28.200000  grains,  weight  of  1  lea. 

25  grains,  weight  of  1  lea  of  40's  yarn. 


3.2,  or  3^  grains,  loss  in  working  1  lea. 


7  leas,  1  hank. 


22.4  grains,  loss  in  working  1  hank. 
40  hanks,  ISb. 
grains.  

1  oz.  is  equal  to  437.5)896.0(2  oz.,  0  dwts.,  21  grains,  loss  sus- 


When  30  inches  of  feed-cloth  is  the  length,  any  given  weight 
of  cotton  is  fed  on  at  the  lap  machine.  The  table  on  the  next 
page  will  show  the  multipliers  for  any  number  of  yards  weighed 
at  any  operation. 

The  number  of  grains  in  any  operation,  multiplied  by  the 
figures  opposite  the  number  of  yards  weighed,  will  give  the  gross 
weight,  from  which  subtract  the  net  weight.  The  difference  will 
be  the  loss  sustained  in  working  the  length  weighed. 


8750 


tained  in  working  lib. 


21.0 


244 


LOSS  IN  WORKING. 


TABLE  OF  MULTIPLIERS. 

For  ascertaining  the  loss  sustained  in  working  any  given 
length  or  weight  of  cotton  yarn,  as  1  lea,  1  hank,  or  IK).,  as 
shown  in  a  preceding  example. 


Length  weighed. 

Multipliers. 

Yards. 

1 

1.2 

2 

2.4 

3 

3.6 

4 

4.8 

5 

6 

6 

7.2 

7 

8.4 

8 

9.6 

9 

10.8 

10 

12 

20 

24 

30 

36 

40 

48 

50 

60 

60 

72 

70 

84 

80 

96 

90 

108 

100 

120 

110 

132 

or  120 

144 

Leas 

2 

288 

3 

432 

4 

576 

5 

720 

6 

864 

ik,  or  7 

1008 

N.  B. —  Where  30  inches  is  the  length  any  given  weight  of  cotton 
is  fed  on  the  feed-cloth  at  lap  machine  {ivhich  is  nearly  gene- 
ral), the  above  multipliers  answer  without  exception. 

The  proportion  of  the  hank,  and  the  weight  of  any  given 
length,  will  be  sufficiently  explained  in  the  foregoing  rules,  ex- 
amples, and  illustrations.    However,  it  will  not  be  out  of  place 


LOSS  IN  WORKING.  245 

to  give  one  or  two  more,  as  nothing  in  calculations  is  more  essen- 
tial to  masters  or  managers. 

According  to  a  former  example,  30  inches  of  roving  weighs 
1.88  grains  (but  no  person  can  weigh  to  so  great  a  nicety).  I 
wish  to  know  what  30  yards  of  the  same  roving  will  weigh,  and 
what  hank  it  is. 

1.88  grains,  weight  of  30  inches  of  roving. 
36  multiplier  for  30  yards  (see  Table). 

1128 
664 


67.68  grains,  or  2  dwts.,  19.68  grs.,  weight 
of  30  yards  of  roving. 

250  is  the  dividend  for  30  yards,  which,  divided  by  the  number 
of  grains  it  weighs,  will  give  the  hank  roving. 

grains.  Dividend. 
Weight  of  30yards,  67.68)250.00(3.693,  or  3/g  hank  rov.  nearly. 

20304 


46960 
40608 


63520 
60912 


26080 
20304 


5776 

If  the  hank  roving  when  weighed  be  4|  or  4.166  hanks,  what 
will  be  the  loss  sustained  in  working  30  yards  ? 

250  is  the  dividend  for  30  yards,  which,  divided  by  4.166,  the 
hank  roving,  will  give  the  number  of  grains  net  weight. 

Hank  roving,  =  4. 166)250. 000(60  grains,  net  weight  of  30  yards, 
25000  of  41  hank  roving. 

N.  B. — For  loss  sustained  in  working,  see  next  example. 


246 


LOSS  IN  WORKING. 


If  the  weight  of  cotton  required  for  30  yards  of  roving  be 
67.68  grains,  and  the  weight  of  the  same  length  of  roving  be  60 
grains,  which  is  equal  to  4.166  or  4|  hanks,  what  will  the  loss 
sustained  in  working  be  for  1  lea,  1  hank,  and  1ft).  ? 

67.68  grs.,  weight  of  cot.  req'd  for  30  yds.  of  rov. 
60      grains,  weight  of  30  yards  of  roving. 

7.68  grains,  loss  at  30  yards. 

4  times  30  is  equal  to  120  yards,  or  1  lea. 

30.72  grains,  loss  at  1  lea. 
7  leas,  1  hank. 

215.04  grains,  loss  at  1  hank. 
4.166  hank  roving  produced. 


129026 
129026 
21504 
86016 


895.85686  grains,  loss  sustained  in  working  1ft).  of 

cotton. 

Or, 

1  oz.  is  equal  to  437.5  grs.)895.85686(2.0477  ounces. 

8750  437|  grains  are  1  oz. 

20856  3339 
17500  1431 
  1908 

33568  238 

30625   

  20.8687  grains,  or  2  oz. 

29436   0  dwts.,  21  grs. 

30625 — nearly.  nearly. 


AVERAGE  COP,  ETC. 


247 


AVERAGE  COP  AND  WEIGHT  OF  SETS. 

To  find  the  numbers  of  yarn  and  the  number  of  hanks  in  one 
set  of  cops  (from  an  average  cop),  the  weight  of  the  set  being 
given. 

RULE. — Multiply  the  length  on  one  cop  by  the  number  of  spin- 
dles in  the  wheels  for  the  number  of  hanks  in  the  set ;  then 
divide  by  the  weight  of  the  set,  and  the  quotient  will  be  the 
numbers  of  yarn. 

If  a  set  of  cops  from  a  pair  of  wheels  containing  808  spindles 
weighs  30  lbs.,  and  the  length  on  one  cop  be  1  hank,  6  leas,  and 
70  threads,  what  number  of  hanks  will  there  be  in  the  set,  and 
what  number  of  yarn  will  it  be 

Hank.    Leas.  Threads. 
One  cop  contains   1    .  .    6    .  .  70 

10  X  10  X  8  add  8=808  spdls. 


19    . .    5    .  .  60 

10 


198    .  .    1    .  .  40 

8 


1585    .  .    5    .  .  0 
15    .  .    6    .  .  0=8 

^Sht-°^sets  I  .  .    4    .  .    0  No.  of  hanks  on  1  set. 

53.4  nearly,  hanks  fineness  of  Nos.  of  yarn. 

Or, 

Reduce  the  length  on  one  cop  to  threads,  and  multiply  by  the 
number  of  spindles  in  the  wheels ;  then  divide  by  the  number  of 
threads  in  one  lea,  the  quotient  of  which  must  be  divided  by  the 
number  of  leas  in  one  hank,  and  that  quotient  will  be  the  number 
of  hanks  contained  in  the  set;  then  the  number  of  hanks  con- 
tained in  the  set  must  be  divided  by  the  weight  of  set,  and  the 
quotient  will  be  the  number  of  hanks  in  lib. 


248 


AVERAGE  COP,  ETC. 


Hank.  Leas.  Threads. 
One  cop  contains  1  .  .  6  .  .  70 
7  leas,  1  hank. 


13 

80  threads,  1  lea. 


1110  threads  on  one  cop. 
808  spindles  in  the  pairs  of  wheels. 

8880 
88800 


1  lea,  8.0  thrds.)89688.0  threads  on  1  pair  of  sets. 

1  hank,  7  leas,)11211  leas  on  one  pair  of  sets. 

1601.5714  hanks  on  1  pair  of  sets. 
7  leas,  1  hank. 

3.9998  leas. 

80  threads,  1  lea. 


79.9840  threads. 

The  length  of  yarn  on  one  pair  of  sets  will  be  1601  hanks,  4 
leas. 

Weight  of  set,  3.0  ibs.)160. 1.5714  hanks  on  one  pair  of  sets. 

53.3857,  or  rather  more  than  53^  Nos. 

of  yarn. 

What  will  one  set  of  cops  weigh,  if  the  wheels  contain  808 
spindles,  the  numbers  of  yarn  53  hanks  to  the  pound,  the  num- 
ber of  stretches  1000,  and  the  length  of  the  stretch  put  up  60 
inches? 

Multiply  the  number  of  stretches,  the  length  of  stretch,  and 
the  number  of  spindles  in  the  wheels  together  respectively  for  a 
dividend ;  then  multiply  the  numbers  of  yarn  by  840  and  36 
respectively  for  a  divisor,  and  the  quotient  will  be  the  weight  of 
the  set. 


AVERAGE  COP,  ETC. 

1000,  Rumber  of  stretches  on  one  cop. 
60  inches,  length  of  stretch. 

60000 

808       number  of  spindles  in  wheels. 


48480000  dividend. 

840  yards,  1  hank. 
36  inches,  1  yard. 

5040 
2520 


30240  inches  in  1  hank. 
63,  numbers  of  yarn. 


00720 
151200 


1602720  divisor. 

1602720)48480000(30ibs.,      oz.,  weight  of  set. 
4808160 


398400 

16  ounces,  lit). 


2390400 
398400 


1602720)6374400(3  ounces. 
4808160 


1566240 

4  qrs.,  1  ounce. 


1602720)6264960(3  qrs. 
4808160 


1456800 


250  AVERAGE  COP,  ETC. 

What  -will  the  "weight  of  one  pin  or  shuttle-cop  of  86's  weft 
be,  containing  450  stretches,]each  stretch  57  inches  net  (allowed 
for  breakage). 

450,  number  of  stretches  on  cop. 
57  inches,  length  of  stretch. 


3150 
2250 


1  yard  is  36  inches,)25650(712.5  yards. 
252 

45 

36 


90 
72 


180 
180 

1  lea  is  120  yards,)71 2.5(5.9375  leas  on  1  cop. 
600 


1125 
1080 


450 
360 


900 
840 


600 
600 


AVERAGE  COP,  ETC.  251 

Leas. 

Nos.  of  weft,  36's)5.937. 5(164.93  grains,  or  6  dwts.,  20.93  grs., 
36  weight  on  1  cop. 


233 
216 


177 
144 


335 
324 


110 
108 


2 

How  raany  leas  and  threads  are  there  in  one  cop,  containing 
7121  yards  ? 

1  lea  is  120  yards, )712. 5(5  leas,  75  threads,  on  1  cop. 
600 


IJ  yards  is  1  thread,  1.5)112.5(75  threads. 

105 


75 
75 

B. — In  ascertaining  the  weight  of  one  cop,  recJcon  your  divi- 
dend as  many  thousands  as  you  have  leas;  and  ivhere  the  deci- 
mal of  a  lea  occurs,  ^vhich  is  generally  the  case,  put  the  point 
in,  reserving  the  tliousands,  which,  divided  by  the  numbers  of 
yarn,  will  give  the  weight  of  the  cop  in  grains. 

What  will  one  cop  of  36's  twist  weigh,  containing  900 
stretches,  each  stretch  61 J  inches,  exclusive  of  breakage? 


252  AVERAGE  COP,  ETC. 


900,  number  of  stretches. 
61.5    or  GIJ  inches,  length  of  stretch. 


r  6)55350.0 

1  yard  is  36  inches,  <  

t  6)9225 


1  lea  is  12,0  yards,)153.7.5  yards  on  1  cop. 


12.8125  leas  on  1  cop. 

Nos.  of  yarn,  36)12812.5(355.9  grains,  or  14  dwts.,  19.9  grains, 
108  weight  of  1  cop. 


201 
180 


212 
180 

325 
324 


What  ■will  one  cop  of  48's  twist  weigh;  if  it  contains  1200 
stretches,  each  stretch  to  put  up  61  inches,  exclusive  of  breakage? 

1200,  number  of  stretches. 
61  inches,  length  of  stretch. 


1200 
7200 


1  yard  is  86  inches, 


j  6)73200  inches  on  1  cop. 
1^6)12200 


1  lea  is  12.0  yards,)203.3.3  yards  on  1  cop. 


16-944  leas,  or  2  hanks,  2.944  leaa 
—   on  1  cop. 


WEIGHT  OF  SETS.  253 

Leas, 
r  4)16.944 

Nos.  of  yarn,  i8<  

[12)4236 


353,  grains,  or  14  dwts.,  17  grains,  weight 
  of  1  cop. 


WEIGHT  OF  SETS. 

The  number  of  hanks,  and  weight  of  a  pair  of  sets  of  cops, 
are  required  from  the  following  particulars: — 

Number  of  spindles,  1008. 
Number  of  stretches,  900. 
Length  of  stretches,  61|-  inches. 
Numbers  of  yarn,  36  hanks  to  1  lb. 

1008  number  of  spindles  in  mules. 
900,  number  of  stretches. 


907200 

61.5,  or  61|  inches,  length  of  stretch. 


4536000 
907200 
5443200 


55792800.0  inches  of  yarn  on  1  pair  of  sets. 

1  yard  is  36  inches,)55792800(1549800  yards  on  1  set  of  cops. 
36 


197 
180 


179 
144 


352 
324 


288 
288 


254  WEIGHT  OP  SETS. 

1  lea  is  12.0  ycls.)154980.0  yards  on  1  set  of  cops. 


1  hank  is  7  leas,)12915  leas  on  1  set  of  cops. 
Nos.  of  yarn,  36,  ■ 


r  6)1845  hanks  on  1  set  of  cops. 


6)307.5 

51.25  lbs.,  or  51  lbs.,  4  oz.,  weight  of  set. 
16  ounces  1  lb. 


150 
25 


4.00  ounces. 

The  number  of  hanks  in  a  pair  of  sets  of  cops  is  required 
from  the  following  particulars:  — 

Number  of  spindles  in  mules,  1340. 
Number  of  stretches,  1200. 
Length  of  stretches,  59.5  inches. 

1840  spindles  in  mules. 
1200  stretches. 


1608000 

59.5,     or  59-J  inches,  length  of  stretch. 


8040 
14472 

8040 


1  yd.  is  36  in. 


(  6)95676000.0  yards  of  yarn  on  1  set  of  cops. 
\  6)15946000 


1  lea  is  12.0  yds,)265766.6.6  yards  of  yarn  on  1  set  of  cops. 
1  hank  is  7  leas,)22147.222  leas  of  yarn  on  1  set  of  cops. 


3163.888  hanks  of  yarn  on  1  set  of  cops. 


spinner's  book,  etc. 


255 


-3163.888  hanks  of  yarn  on  1  set  of  cops. 
7  leas,  1  hank. 


6.222  leas. 

120  yards,  1  lea. 

26.666  yards. 

SPINNER'S  BOOK,  &c. 

Where  it  is  customary  to  pay  the  spinners  at  the  rate  of  so 
much  per  thousand  hanks,  the  length  of  the  average  cop  from 
each  set  may  be  put  down  for  the  week;  then  add  them  together 
and  multiply  by  the  number  of  spindles  in  the  mules,  as  follows: 


Number  of  spindles 
in  mules. 

Weight 

of  sets. 

Average  cop. 

lbs. 

oz. 

hanks. 

leas. 

threads. 

1008 

51 

8 

5 

65 

50 

4 

4 

72 

52 

6 

6 

36 

51 

12 

5 

60 

51 

10 

5 

14 

52 

8 

6 

10 

52 

4 

5 

32 

51 

12 

5 

64 

52 

4 

6 

38 

52 

8 

6 

14 

51 

0 

5 

0 

50 

4 

4 

18 

Total  for  1  week. 

620 

4 

23 

Hanks.    Leas.  Threads. 
21    ..    4    ..  23 
7  leas,  1  hank. 


151 

80  threads,  1  lea. 

12108 
1008  spindles  in  mules. 

^6824 


256 


spinner's  book,  etc. 


96824 
1210300 


Threads  in  1  lea,  8.0)1219982.4  threads. 


1  hank  is  7  leas,)152497..64,  or  152497  leas,  64  threads. 

21785 . .  2 . .  64,  or  21785  hanks,  2  leas,  64 
threads,  number  of  hanks  on  1  pair  of  sets  of  cops. 
Total  weight,  620  lbs.  )21785(35  J  hanks,  average  number  of  yarns. 
1860 


3185 
3100 


85 

The  number  of  hanks  per  spindle  will  be  ascertained  by  di- 
viding the  number  of  hanks  spun,  by  the  number  of  spindles  in 
the  mules,  or  throstles. 

If  the  total  number  of  hanks  spun  in  a  week  be  21745,  and 
the  number  of  spindles  in  the  mules  be  1008;  what  number  of 
hanks  per  spindle  will  be  produced? 

1008)21745(21.5724,  or  21  hanks,  4  leas  per  spindle. 
2016  7  leas,  1  hank. 


1585  4.0068  leas. 

1008         120  yards,  1  lea. 


5770  .8160 
6040 


7300 
7056 


2440 
2016 


4240 
4032 


208 


DRESSING  MACHINE. 


257 


The  spinner's  book  should  be  made  up  so  that  the  weight,  num- 
bers of  yarn,  the  total  number  of  hanks,  and  the  number  of  hanks 
per  spindle  per  week,  would  appear  at  one  view,  for  the  satisfac- 
tion of  the  employers,  and  the  government  of  the  managers. 


THE  FOLLOWING  FORM  MIGHT  BE  ADOPTED. 


Date. 
1S39. 

April 
17 

Name. 

Weight. 

lbs. 

Number. 

Total  number 
of  hanks 

No.  of  hanks 
per  spindle. 

Rale. 

£     s.  d. 

John  Pollard. 

620 

35i 

21745 

21.3724 

2      8  U 

iV.  B. —  The  form  of  the  book  may  he  altered  according  to  the  sys- 
tem of  spinning  and  paging,  but  the  above  particulars  should 
always  appear. 

DRESSING  MACHINE. 

Dressing  machines  are  of  various  constructions,  and,  like  most 
other  machines,  have  been  greatly  improved  ;  however,  the  neces- 
sary calculations  will  be  easily  ascertained  from  the  following 
examples. 

The  speed  of  the  crank-shaft,  on  which  is  fixed  the  top,  or 
large  cone  drum,  is  required  from  the  following  particulars : — 

Revolutions  of  driving-shaft  a  minute,  66. 
Diameter  of  drum  on  shaft,  18  inches. 
Diameter  of  pulley  on  crank-shaft,  17J  inches. 

66  revolutions  of  driving-shaft  a  min. 
18,  diameter  of  drum  on  driving-shaft. 

528 
66 


1188 


258 


DRESSING  MACHINE. 


In.  diam.  of  pul.  \  i7.5)ii88(67.885714  revolutions  of  crank 
on  crank-snait,    j         -inrA      ^  ■    ^         i  ■  i  ■  c  i 

'   ■'  lUoO     shait  a  minute,  on  which  IS  nxed. 

 the  top,  or  large  cone  drum. 

1380 

1225 


1550 
1400 


1500 
1400 

1000 
8T5 

1250 
1225 


250 
175 

750 
700 

50 

The  speed  of  the  fan  at  dressing  machine  is  required  from  the 
following  particulars: — 

Revolutions  of  crank-shaft  a  minute,  67.885714. 

Diameter  of  pulley  on  crank-shaft  for  driving  fan,  25  inches. 

Diameter  of  pulley  on  the  end  of  fan,  2  inches. 

67.885714  revols.  of  crank-shaft  per  min, 
25  in.,  diam.  of  pul.  on  crank-shaft. 


339428570 
135771428 


In  diam  of  pul.  12)1697.142850 
on  the  end  oi  tan,  j  ^  


848.571425  revolutions  of  fan  a  minute. 

The  speed  of  the  fan  at  dressing  machine  is  required  from  the 
following  particulars : — 


DRESSING  MACHINE. 


259 


Revolutions  of  driving-shaft  a  minute,  66. 

Diameter  of  drum  on  shaft,  18  inches. 

Diameter  of  drum  on  crank-shaft,  ITJ  inches. 

Diameter  of  pulley  on  crank-shaft  for  driving  fan,  25  inches. 

Diameter  of  pulley  on  end  of  fan,  2  inches. 

66  revolutions  of  driving-shaft  a  min. 
18  inches,  diam.  of  drum  on  driving-shaft. 

528 
66 


1188 

25  inches,  diam.  of  pulley  on  crank-shaft 


5940 
2376 


for  driving  fan. 


29700  dividend. 


17.5  inches,  diameter  of  pulley  on  crank-shaft. 
2  inches,  diameter  of  pulley  on  end  of  fan. 


35.0  divisor. 


35  < 


r  5)29700 


(  7)5940 

848.571428  revolutions  of  fan  per  minute. 

If  the  fan  of  a  dressing  machine  makes  848.571428  revolu- 
tions a  minute,  and  its  diameter  is  18  inches;  how  many  yards 
"will  it  traverse  a  minute  ? 


848.571428  revolutions  of  fan  a  minute. 
1.5  foot,  =  18  in.  diam.  of  fan. 


4242857140 
848571428 


1272,8571420 


260 


DRESSING  MACHINE. 


1272.8571420 

3.1416  circum.  when  the  diam  is  1. 


7637142852 
1272857142 
5091428568 
1272857142 
3818571426 


1  yard  =  3  feet)3998.8079973072  feet,  fan  traverses  a  minute. 


1332.93566576906  yards,  fan  traverses  a  min. 

The  fan  of  a  dressing  machine  (as  in  the  above  example)  will 
traverse  a  space  equal  to  1333  yards  nearly. 

The  speed  of  the  under  cone  drum  is  required  from  the  follow- 
ing particulars : — 

Revolutions  of  crank,  or  top  cone  drum-shaft,  67.885714  a  min. 
Diameter  of  top  cone  drum,  llf  inches. 
Diameter  of  bottom  cone  drum,  4f  inches. 

67.885714  revols.  of  top  cone  drum-shaft  a  min. 
11.75,  or  llf  inches,  diam.  of  top  cone  drum. 

339428570 
475199998 
746742854 


797.65713950  dividend. 

Diam.  of  under  cone  drum, 4.75in.)797.6571395(167.9278  revols. 

475  of  under  cone  drum 

  a  min. 

3226 
2850 


3765 
3325 


4407 
4275 


1321 

950 


3713 
3325 


3889 
3800 


DRESSING  MACHINE.  \     .   "  261 

iV.  B. —  The  preceding  example  shows  the  greatest  speed!  that,  the 
under  cone  drum  can  work  ;  the  largest  diameter  of  the  top  coney 
and  the  smallest  diameter  of  the  under  cone  being  given,  i.  e., 
the  greatest  speed  that  can  be  given  to  the  motions  connected 
with  the  top  beam  on  which  the  dress  yarn  is. 

The  speed  of  the  top  beam  can  be  regulated  by  a  worm,  or 
screw-shaft,  which  works  the  strap  on  the  drums,  and  must  be 
done  according  to  the  heat,  or  drying,  and  fineness  of  yarns. 

The  speed  of  the  top,  or  dressed  yarn  beam,  is  required  from 
the  following  particulars. 

Revolutions  of  under  cone-shaft  a  minute,  167.9278. 

Wheel  on  the  end  of  cone-sliaft,  74  teeth. 

Wheel  on  foot  of  upright-shaft,  44  teeth. 

Single  worm  on  top  of  upright-shaft. 

Wheel  on  shaft  for  working  top  beam,  68  teeth. 

167.9278  revols.  of  under  cone  drum  a  min. 
74  teeth  wheel  on  the  end  of  do. 


6717112 
11754946 


12426.6572  dividend. 

44  teeth,  wheel  on  foot  of  upright-shaft. 

68  teeth,  wheel  on  shaft  for  working  top  beam. 


352 
264 


2992  divisor. 

2922)12426.6572(4.1533  revols.  a  min.  of  top, 
11968  or  dressed  yarn  beam,  at 
  the  bottom  or  beginning. 


4586 
2992 

15945 
14960 

9857 
8976 


8812 

8976— nearly. 


262 


DRESSING  MACHINE. 


JW  B. —  The  top,  or  dressed  yarn  beam,  decreases  in  speed  as  it 
Jills,  continuing  to  traverse  over  the  same  surface  as  at  the  com- 
me7icement,  so  that  the  yarn  is  dried  regularly. 

If  the  heat,  or  drying  increases,  or  decreases,  which  is  some- 
times the  case,  then  the  top,  or  dressed  yard  beam,  must  be  regu- 
lated in  speed  accordingly,  which  will  be  done  by  moving  the 
strap  on  the  cone  drums  by  the  worm,  or  screw  attached  for  that 
purpose. 

PARTICULARS  OF  DRESSING  FRAME. 

Revolutions  a  min.  of  crank,  or  top  cone  drum-shaft,  67.885714. 
Revolutions  of  fan  a  minute,  848.571425. 

Revolutions  of  under  cone  a  minute,  at  the  bottom  of  beam, 
167.9287. 

Revolutions  of  top,  or  dressed  yarn  beam  a  minute,  at  the  bottom 

of  beam,  4.1533. 
Diameter  of  pulley  on  crank,  or  top  cone  drum-shaft,  17J  inches. 
Diameter  of  pulley  on  crank,  or  top  cone  drum-shaft  for  driving 

fan,  25  inches. 
Diameter  of  pulley  on  end  of  fan,  2  inches. 
Diameter  of  fan,  18  inches. 
Diameters  of  top  cone  drum,  11}  and  6  inches. 
Diameters  of  under  cone  drum,  10^  and  4f  inches. 
Radius  of  crank  for  brushes,  3  inches. 
Radius  of  crank  for  leverage.  If  inch. 
Traversing  of  fan  a  minute,  1333  yards,  nearly. 

iV".  B. —  The  dimensions  of  the  cone  drums  are  the  tivo  extremes. 

What  number  of  ends  must  there  be  on  each  twist  beam,  allow- 
ing 8  beams  to  a  machine,  i.  e.  4  beams  to  each  side,  to  produce 
a  piece  of  cloth  29i  inches  wide,  in  a  72  reed,  Manchester  and 
Stockport  count  ? 

29.5,  width  of  warp  at  the  end. 
72  reed,  Manchester  &  Stockport  count. 


690 
2065 


Number  of  beams,  8)2124.0  total  number  of  ends  in  the  warp. 


265.5  number  of  ends  on  each  beam. 


POWER-LOOM. 


263 


N.B. —  The  numher  of  ends  required  for  each  beam  is  265.5, 
which  may  he  made  into  266,  and  make  two  twisters,  or  double 
ends  at  the  selvage,  at  each  side  of  the  machine. 

What  number  of  ends  will  it  require  to  produce  a  top,  or  dressed 
yarn  beam,  to  fill  b\\  inches  in  an  84  reed,  Manchester  and  Stock- 
port count ;  and  what  number  of  ends  must  there  be  on  each  twist 
beam,  allowing  8  twist  beams  to  a  machine  ? 

51.5  in.,  width  of  top,  or  dres'd  yarn  bm.  at  reed. 
84  reed,  Manchester  and  Stockport  count. 


2060 
4120 


Num.  of  bms. 8)4326.0  number  of  ends  in  dressed  yarn  beam. 

540.75  number  of  ends  required  on  each  twist  bm. 

N.  JB. — Add  as  many  ends  as  are  required,  according  to  the 
number  of  double  ends  loanted  at  the  selvages. 

If  there  be  542  ends  on  a  twist  beam,  and  8  beams  to  a  ma- 
chine; how  many  ends  will  there  be  in  the  dressed  yarn  or  top 
beam  ? 

542  ends  on  each  twist  beam. 
8  beams  to  a  machine. 


4386  ends  on  dressed  yarn,  or  top  beam. 

N.  B. —  The  bell  wheel  at  the  dressing  machine  must  be  regulated 
according  to  the  size  of  your  under  roller,  and  length  of  inece 
required. 


POWER-LOOM. 

The  number  of  picks  a  minute  is  required  from  the  following 
particulars : — 

Revolutions  of  driving-shaft  a  minute,  102. 
Diameter  of  drum  on  driving-shaft,  14  inches. 
Diameter  of  pulley  on  loom,  11  inches. 


264 


POWER-LOOM. 


102  revols.  of  driving-shaft  a  min. 
14  in.  diam.  of  drum  on  same  shaft. 


408 
102 


In.  diam.  of  pul.  on  loom,  11)1428 

129.818  number  of  picks  a  mln. 

If  the  crank-shaft  of  a  loom  makes  129.818  revolutions  a 
minute,  with  a  wheel  50  teeth  fixed  on  the  end,  working  into  a 
wheel  with  100  teeth  on  the  end  of  the  tappet-shaft;  what  num- 
ber of  revolutions  will  the  tappet-shaft  make  a  minute  ? 

129.818  revolutions  of  crank-shaft  a  min. 
50  teeth  on  end  of  crank-shaft. 

Teeth  on  end  of  1  ioO)6490.900 
tappet-shait,    J  '  

64.909  revolutions  a  min.  of  tapt. -shaft. 

N.B. — Tlie  above  examples  only  refer  to  plain  cloths,  but  the 
calculations  of  ttvills,  fustians,  and  all  other  fancy  goods,  are 
regulated  by  the  number  or  different  constructions  of  the  tappets 
tvorJcing  upon  the  treadles,  or  levers,  connected  with  the  healds, 
whereby  nearly  any  pattern  may  be  constructed  and  manufac- 
tured as  by  hand-weaving. 

The  number  of  picks  a  minute  is  required  from  the  following 
particulars : — 

Revolutions  of  driving-shaft  a  minute,  98.25 
Diameter  of  drum  on  driving-shaft,  15.5  inches. 
Diameter  of  pulley  on  crank-shaft,  12.75  inches. 

98.25  revolutions  of  driving-shaft  a  minute. 
15.5,  or  15J  in.  diam.  of  drum  on  driving-shaft. 

49125 
49125 
9825 


1522.875  dividend. 


POWER-LOOM. 


265 


12.75)1522.875(119.441  revolutions  of 
1275  crank- shaft 

•  ■  a  minute. 

2478 
1275 


12037 
11475 


5625 
5100 


5250 
5100 


1500 
1275 


225 

The  speed  of  the  tappet-shaft  is  required  from  the  following 
particulars : — 

Revolutions  of  crank-shaft  a  minute,  119.441. 
Wheel  on  end  of  crank-shaft,  50  teeth. 
Wheel  on  end  of  tappet-shaft,  100  teeth. 

119.441  revols.  of  crank-shaft  a  min. 
50  teeth,  •wheel  on  crank-shaft. 

Whl.  on  tapt.-shft.  100  tth.)5972.050 

69.7205  revolutions  of  tappet-shaft 

a  minute. 

If  the  crank-shaft  of  a  power-loom  makes  129.818  revolutions, 
i.  e.  picks,  a  minute;  what  time  will  he  required  to  work  suc- 
cessively, to  produce  a  piece  of  cloth  29  yards  long,  with  88 
picks,  or  threads  in  1  inch? 
18 


Inches  diam.  of  pulley  ) 
on  crank-shaft,  12|,  ) 


\ 


266 


POWER-LOOM. 


29  yards,  length  of  piece. 

37  inches,  length  hooked  for  1  yard. 


203 
87 

1073  number  of  inches  in  1  pick. 
88  number  of  picks  in  1  inch. 


8584 
8584 


Dividend  94424  total  number  of  picks  in  1  piece, 

29  yards  long. 

Num.  of  picks  a  min.,  129,818)94424.00(727.3567  mins.  required 

908726       to  work  successively, 

 to  produce  1  piece  of 

355140  cloth,  29  yards  long, 
259636      or  12  hours,  7  mins., 

  21.402  seconds. 

955040 
908726 


463140 
389454 


736860 
649090 


877700 
778908 


987920 
908726 


79194 

The  length  of  time  required  for  the  loom  to  work  successively, 
to  produce  1  piece  of  cloth  29  yards  long  with  88  picks,  or 
threads  in  1  inch,  will  be  12  hours,  7  minutes,  and  21  seconds.  J 
N.  B.—The  distance  of  the  hooks  on  all  frames  for  hooking  pieces 

is  37  inches. 


POWER-LOOM. 


26T 


If  the  crank-shaft  of  a  power-loom  makes  119.441  revolutions 
a  minute,  i.  e.  so  many  picks  or  threads;  what  length  of  time 
must  it  work  successively,  to  produce  a  piece  of  cloth  29  yards 
•long  with  84  picks,  or  threads  in  1  inch? 

29  yards,  length  of  piece. 

37  inches,  length  hooked  for  1  yard. 


203 
87 


1073  number  of  inches  in  1  piece  of  cloth. 
84  number  of  picks  or  threads  in  1  inch. 

4292 
8584 


Dividend  90132  number  of  picks  in  1  piece  of  cloth  29 

yards  long. 

Num.  of  picks  a  min.,  119.441)90132.0(754.615  minutes,  or 

836087  60)754.615 

652330      12.. 34.. 615 
597205  eOs.lm. 


551250  36.900 
477764 


734860 
716646 


182140 
119441 


626990 
597205 


29785 

The  length  of  time  required  for  the  loom  to  work  successively, 
to  produce  a  piece  of  cloth  of  the  foregoing  description,  will  be 
12  hours,  34  minutes,  37  seconds,  nearly. 

The  weight  of  yarn  is  required,  to  make  one  piece  of  cloth,  of 
the  following  description :— 


268 


POWER-LOOM. 


Length  of  piece,  29  yards. 

Count  of  reed,  72.   (Manchester  and  Stockport  count.) 

Numbers  of  twist,  36's. 

Width  of  warp  at  the  reed,  29J  inches. 

Number  of  picks  in  1  inch,  88. 

Number  of  weft,  36's. 

29  yards,  length  of  piece. 

72,  Manchester  and  Stockport  count  of 
  reed. 

58 
203 


2088 

29J  inches,  width  of  warp  at  the  reed. 


18792 
4176 
1044 


1  hank  is  840  yards,)61596(73.328  hanks  of  twist  required  for 
5880  the  piece. 


2796 
2520 


2760 
2520 

  7200 

2400  6720 

1680   

  480 

29  yards,  length  of  piece. 
88  picks  or  threads  in  1  inch. 

232 
232 


2552 

29,5,  or  29|-  inches,  width  at  the  reed. 


12760 


n 


POWEE-LOOM.  26© 

12760 

22968 
5104 

75284.0 

1  hank  is  840  yards,)75284.0(89.624  hanks  of  weft  required 
6720  for  the  piece. 


8084 
7560 


5240 
5040 

2000 
1680 

3200 

3360— nearly. 

73.328  hanks  of  twist. 
89.624  hanks  of  weft. 


{6)162.952  hanks  of  yarn  required  for  1 
  piece. 
6)27.158 

4.526  ft)S.  of  yarn. 
16  oz.,  1  ft). 


3156 
526 


8.416  ounces. 

4  qrs.  1  ounce. 


1.664  qrs. 

The  weight  of  yarn  required  for  the  piece  is  4  fts.  oz., 
nearly. 

Or, 

When  the  numbers  of  twist  and  weft  are  the  same,  the  question 
may  be  worked  in  one  operation,  by  adding  the  Manchester  or 


270 


POWER-LOOM. 


Stockport  count  of  reed,  and  the  number  of  picks,  or  threads  re- 
quired in  the  inch  together,  and  then  proceed  as  in  either  of  the 
last  examples. 

Tims, 

72,  Manchester  or  Stockport  count  of  reed. 
88  picks,  or  threads  in  1  inch. 

160 

29  yards,  length  of  piece. 


1440 
320 


4640 

29.5  inches  width  at  the  reed. 


23200 
41760 
9280 


136880.0  dividend. 

Yards  in  1  hank,  840 
Numbers  of  yarn,  36 


5040 
2520 


Yards  in  1  ft.,  30240)136880.0(4.526  lbs.  of  yarn. 
120960 


159200 
151200 


80000 
60480 


195200 
181440 


13760 

The  weight  of  yarn  required  for  the  piece  is  4  lbs.,  8|  oz., 
nearly  as  in  the  last  example. 


WHEELS  REQUIRED  TO  PRODUCE  ANT  GIVEN  DRAUGHT.  271 


THE  DRIVING  AND  DRIVEN  WHEELS  REQUIRED  TO  PRODUCE  ANY 
GIVEN  DRAUGHT  BETWEEN  THE  MIDDLE  AND  BACK  ROLLERS, 
AND  BETWEEN  THE  BACK  AND  FRONT  ROLLERS,  THE  DIAMETER 
OF  THE  ROLLERS  BEING  GIVEN. 

WHEELS  REQUIRED  TO  PRODUCE  ANT  GIVEN  DRAUGHT  FOR  BACK 
AND  MIDDLE  ROLLERS. 

RULE. — Multiply  the  length  you  intend  drawing,  by  the  di- 
ameter of  the  middle  roller,  for  the  driving-wheel ;  and  the  length 
you  wish  that  drawn  into,  by  the  diameter  of  the  back  roller,  for 
the  driven-wheel. 

If  a  greater  or  less  number  of  teeth  be  required  in  the  wheel, 
divide  the  driver  and  driven-wheels  by  any  number  that  will  di- 
vide both  without  a  remainder ;  then  multiply  the  quotients  by 
any  number,  according  to  the  number  of  teeth  wanted  in  the 
wheels. 

iV.  B. — The  diameter  of  the  ivheels  to  ill  he  according  to  the  pitch 
of  the  teeth. 

What  number  of  teeth  must  there  be  in  the  wheel  required, 
for  the  back  and  middle  rollers  to  produce  a  draught  of  1  into  2, 
allowing  the  back  roller  to  be  |  inch,  and  middle  roller  1  inch 
in  diameter  ? 

1  into  2  draught 
Middle  roller  1  inch,  or  8        7,  or  |  inch  back  roller. 

Divided  by  2)8  14 

Quotients  4  and  7 
Multipliers  5  5 

Mid.  rol.,  driving-wheel  20tth.  35  teeth,  driven-wheel. 

Required  the  draught  between  the  middle  and  back  rollers, 
from  the  following  particulars  : — 

Wheel  on  middle  roller,  (driving-wheel,)  20  teeth. 
Wheel  on  back  roller,  (driven-wheel,)  35  teeth. 
Diameter  of  middle  roller,  1  inch. 
Diameter  of  back  roller,  ^  inch. 


272     WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 

Driving-wheel.  Driven-wheel. 
In  diam  of  1  teeth.  35  teeth, 

backroller'.,  U  J_  ^        ^^i^^-  «f  '^'^'^^^  ^<^^- 

140  140)280(2,  or  1  into  2  draught, 

280     between  middle  and 
back  rollers. 

What  number  of  teeth  must  there  be  in  the  wheels  on  the  back 
and  middle  rollers,  to  produce  a  draught  equal  to  2  into  3,  if  the 
back  roller  be  |  inch,  and  the  middle  roller  1  inch  in  diameter? 

2  into  3  draught, 
Middle  roller,  1  inch,  or  8        7,  or  |  inch  back  roller. 

Middle  roller  wheel,  16       21  wheel  on  back  roller. 
2  2 

Middle  roller  wheel,  32  tth.  42  teeth,  wheel  on  back  roller. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars:  — 

Driving-wheel.  Driven-wheel. 
16  teeth.    21  teeth. 
Diameter  of  back  roller,  7  8,  or  1  inch  diam.  of  mid.  rol. 


112  )168(1.5,  or  2  into  3  draught. 

112 


560 
560 


Or, 

Driving-wheel.  Driven-wheel. 
32  teeth.  42  teeth. 
Diameter  of  back  roller,   7  8,  or  1  in.  diam.  of  mid.  rol. 


224       )336(1.5,  or  2  into  3  draught. 
224 


1120 
1120 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGIJT.  273 

'■/■■_ 

What  number  of  teeth  roust  there  be  in  the  wheels  on  the  back 
and  middle  rollers,  to  produce  a  draught  equal  to  3  into  4,  if  the 
back  and  middle  rollers  be  the  same  diameters  ? 


3  into  4  draught. 
Middle  roller  wheel,  21tth.28  teeth,  back  roller  wheel. 


The  draught  between  the  middle  and  back  roller  is  required 
from  the  following  particulars,  the  diameters  of  the  rollers  being 
the  same: — 

Driving-wheel.  Driven-wheel. 

21  21)28(11  or  3  into  4  draught. 

21 

7 

21 


The  wheels  for  the  back  and  middle  rollers  are  required  to  pro- 
duce a  draught  of  3  into  4,  the  diameter  of  the  back  roller  being 
1  inch,  and  the  middle  roller  1|-  or  |  inch  diameter : — 

3  into  4  draught. 
Middle  roller,  |  inch  9         8,  or  1  inch  back  roller. 

,    27  tth.  32  teeth,  wheel  for  back  roller. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars  : — 

Wheel  on  middle  roller,  27  teeth.  Diam.  of  middle  roller,  1 J  inch. 
Wheel  on  back  roller,  32  teeth.   Diameter  of  back  roller,  1  inch. 

Driving-wheel.  Driven-wheel. 
27  teeth.  32  teeth. 
Back  roller  1  inch,  or    8  9,  or  1\  inch,  middle  roller. 


216         )288(li  or  3  into  4  draught. 
216 


72 
216 


« 


274    ■WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 

What  wheels  will  be  required  to  produce  a  draught  of  4  into 
5,  between  the  middle  and  back  rollers,  if  the  back  roller  be  f 
inch,  and  the  middle  roller  1  inch  diameter  ? 

4  into  5  draught. 
Middle  roller,  1  inch,  or  8         7,  or  J  inch  back  roller. 

Middle  roller  wheel,  32  tth.  35  teeth,  wheel  back  roller. 

The  draught  between  the  back  and  middle  rollers  is  required 
from  the  following  particulars  : — 

Wheel  on  middle  roller,  32  teeth.  Diam.  of  middle  roller,  1  inch. 
Wheel  on  back  roller,  35  teeth.   Diameter  of  back  roller,  §  inch. 

Driving-wheel.  Driven-wheel. 
32  teeth.   35  teeth. 
Back  roller,  |  inch  or  7  8,  or  1  inch,  middle  roller. 


224         )280(1.25,  or  4  into  5  draught. 
224 


560 
448 


1120 
1120 

What  wheels  will  be  required  to  produce  a  draught  of  5  into 
6,  between  the  middle  and  back  rollers,  if  the  back  roller  be  | 
inch  and  the  middle  roller  1  inch  diameter  ? 

5  into  6  draught. 
Middle  rollers,  1  inch  or  8         7,  or  |  inch,  back  roller. 

Divide  by  2)40  tth.  42  teeth,  wheel  back  roller. 
—  or  — 

Middle  roller  wheel,  20  tth.  21  teeth,  wheel  back  roller. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars : — 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  275 

Driving-wheel.  Driven-wlieel. 
40  teeth.   42  teeth. 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  middle  roller. 


280         )336(1.2  or  5  into  6  draught. 
280 


560 
560 

iV.  B. — The  wheels  may  he  reduced  to  20  and  21,  and  the  draught 
will  he  the  same. 

What  wheels  will  be  required  to  produce  a  draught  of  6  into 
7,  between  the  middle  and  back  rollers,  if  the  back  roller  be  f 
inch  and  the  middle  roller  1  inch  diameter  ? 

6  into  7  draught. 
Middle  roller  1  inch  or  8         T,  or  |  inch  back  roller. 

Middle  roller  wheel,  48  tth.  49  teeth,  wheel  on  back  roller. 

If  there  be  a  wheel  48  teeth  on  the  middle  roller,  working  into 
a  wheel  49  teeth  on  the  back  roller,  and  the  back  roller  be  |  inch, 
and  the  middle  roller  1  inch  diameter  ;  what  will  the  draught  be  ? 

Driving-wheel.  Driven-wheel. 
48  teeth.    49  teeth. 
Back  roller,  |  inch,  or  7  8,  or  1  inch  middle  roller. 


336         )392(li,  or  6  into  7  draught. 

336 


56 

 1 

—  e 

336 

What  wheels  will  it  require  to  produce  a  draught  between  the 
middle  and  back  rollers  of  7  into  8,  if  the  back  roller  be  ^  inch, 
and  the  middle  roller  1  inch  diameter? 


276     WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


7  into  8  draught. 
Middle  roller,  1  inch,  or  8         7,  or  |  inch  back  roller. 

Divided  by  8)56  56 

Lowest  number  7        7  lowest  number. 
3  3 

Middle  roller  wheel  21  tth.  21  teeth,  wheel  back  roller. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars : — 

Wheel  on  the  middle  roller  21  teeth,  working  into  wheel  on  stud 
40  teeth,  which  works  wheel  21  teeth  on  back  roller. 

Diameter  of  the  middle  roller  1  inch,  and  diameter  of  the  back 
roller  ^  inch. 

Driving-wheel.  Driven-wheel. 
21  teeth.    21  teeth. 
Back  roller,  |  inch  7  8,  or  1  inch,  middle  roller. 


147         )168(14,  or  7  into  8  draught. 
147 


21 
147 

What  wheels  will  be  required  for  the  middle  and  back  rollers, 
to  produce  a  draught  of  7  into  8 ;  allowing  the  back  and  middle 
rollers  to  be  the  same  diameters  ? 

7  into  8  draught. 

2  2 

Middle  roller  wheel,  14  tth.  16  teeth,  wheel  back  roller. 

Or, 

7  into  8 

3  3 

Middle  roller  wheel,  21  tth.  24  teeth,  wheel  back  roller. 
Or, 
7  into  8 

4  4 

Middle  roller  wheel,  28  tth.  32  teeth,  wheel  back  roller. 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  277 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  particulars  in  the  last  example : — 

Driving- -wheel.  Driven-wheel. 
teeth. 

14  teeth,)16(14,  or  7  into  8  draught. 
14 

2 

—  or  4. 
14 

21  teeth,)24(li,  or  7  into  8  draught. 
21 

3 

—  or  4. 
21 

28  teeth,)32(li,  or  7  into  8  draught. 
28 

4 

—  or  ^. 

28 

What  wheels  must  there  be  on  the  middle  and  back  rollers,  to 
produce  a  draught  of  8  into  9,  if  the  back  roller  be  ^  inch,  and 
the  middle  roller  |-  inch  diameter? 

8  into  9  draught. 
Middle  roller,  f  inch,  or  6        7,  ov  I  inch,  back  roller. 

Middle  roller  wheel,  3)48  tth.  63  teeth,  back  roller  wheel. 

Middle  roller  wheel,  16  tth.  21  teeth,  back  roller  wheel. 
2  2 

Middle  roller  wheel,  32  tth,  42  teeth,  back  roller  wheel. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars;— 


278    WHEELS  REQUIKED  TO  PRODUCE  ANY  GIVEN  DRAUGnT. 

Driving-wheel.  Driven-wheel. 
Wheel  on  middle  roller,  32  teeth.  42  teeth,  wheel  on  back  roller. 

7  6 


224        )252(li  or  8  into  9  draught. 
224 


28 

 or 


224 


What  wheels  will  be  required  to  produce  a  draught  of  9  into 
10,  between  the  middle  and  back  rollers,  allowing  the  back  and 
middle  rollers  to  be  the  same  diameter  ? 

9  into  10  draught. 
2  2 

Wheel  on  middle  roller,  18  tth.  20  teeth,  wheel  on  back  roller. 

Or, 

9  into  10 

8  3 

Wheel  on  middle  roller,  27  tth.  30  teeth,  wheel  on  back  roller. 

Or, 

9  into  10 
4  4 

Wheel  on  middle  roller,  36  tth.  40  teeth,  wheel  on  back  roller. 

If  there  be  a  wheel  40  teeth  on  back  roller,  and  a  wheel  36 
teeth  on  middle  roller ;  what  draught  will  there  be  if  the  middle 
and  back  rollers  are  the  same  diameter? 

teeth. 

Wheel  on  middle  roller,  86  teeth. )40(1^,  or  9  into  10  draught. 

36 

4 

—  or  J. 
36 


"WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  279 

If  the  back  roller  be  1  inch,  and  the  middle  roller  §  inch  di- 
ameter ;  what  -wheels  will  be  required  to  produce  a  draught  of  9 
into  10,  between  the  middle  and  back  rollers? 

9  into  10 

Middle  roller,  |  inch,  or  7         8,  or  1  inch,  back  roller. 

Middle  roller  wheel,  63  tth.  80  teeth,  wheel  back  roller. 

The  draught  between  the  middle  and  back  rollers  is  required 
from  the  following  particulars: — 

Wheel  on  middle  roller,  63  teeth.  Wheel  on  back  roller,  80  tth. 
Diameter  of  middle  roller,  |  inch.    Diameter  of  back  roller,  1  in. 

Driving-wheel.  Driven-wheel. 
68  teeth.    80  teeth. 
Back  roller,  1  inch,  or  8  7,  or  |  inch  middle  roller. 

504         )560(1^,  or  9  into  ten  draught. 
604 


56 
604 

If  the  back  roller  be  |  inch,  and  the  middle  roller  |  inch  di- 
ameter ;  what  wheels  will  be  required  to  produce  a  draught  of  10 
into  11,  between  the  middle  and  back  rollers? 

10  into  11 

Middle  roller,  |  inch,  or  6  7,  or  |  inch,  back  roller. 

Middle  roller  wheel,  60  tth.  77  teeth,  wheel  on  back  roller. 
Or, 

If  the  back  and  middle  rollers  were  the  same  diameter. 

10  inch  11 
2  2 

Middle  roller  wheel,  20  tth.  22  teeth,  wheel  on  back  roller. 


280    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


Or, 

10  into  11 
3  3 

Middle  roller  wheel,  30  tth.  33  teeth,  wheel  on  back  roller. 

If  the  wheel  on  the  back  roller  be  77,  and  the  wheel  on  the 
middle  roller  60,  and  the  back  roller  |  inch,  and  the  middle 
roller  |  inch  diameter,  required  the  draught? 

Driving-wheel.  Driven-wheel. 
60  teeth.   77  teeth. 
Back  roller,  |  inch,  7  6,  or  f  inch,  middle  roller. 


420         )462(1.1,  or  10  into  11  draught. 
420 


420 
420 

TOTAL  DRAUGHT  IN  ROLLERS. 

KULE. — Multiply  the  diameter  of  the  front  roller  by  any  num- 
ber that  will  produce  a  wheel  of  a  sufficient  diameter  for  the  first 
driving;  then  multiply  the  diameter  of  the  back  roller  by  twice 
the  number  the  front  roller  is  multiplied  by  for  the  first  driven 
wheel,  which  will  produce  a  draught  equal  to  2.  If  a  draught 
of  3  be  required,  multiply  the  diameter  of  the  back  roller  by  3 
times  the  number  by  which  the  front  roller  is  multiplied;  if  any 
intermediate  draught  between  the  whole  numbers  be  required,  as 
2|,  2^,  or  2 J,  add  to  the  product  in  proportion;  and  if  above  3 
of  a  draught  be  required,  proceed  accordingly. 

The  first  driving  and  driven-wheels  being  ascertained,  divide 
the  total  draught  required  by  the  draught  produced ;  the  quotient 
of  which,  multij)lied  by  the  second  driving  wheel,  will  give  the 
second  driven-wheel ;  if  more  wheels  are  required,  they  will  be 
found  in  the  same  way. 

iV.  5. — The  second  driving,  or  change-wheel  may  contain  any 
number  of  teeth,  according  to  the  diameter  required. 

If  larger  or  smaller  wheels  be  required,  they  may  be  increased, 
or  decreased,  in  proportion  to  each  other,  i.  e.,  the  driving  and 
driveu'wheels  must  be  multiplied,  or  divided  by  the  same  number. 


WHEELS  KEQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  281 

If  the  back  roller  be  1  inch,  and  the  front  roller  1|  inch 
diameter ;  what  wheels  will  be  required  to  produce  a  draught  of  6  ? 

Diameter  of  front  roller,  9,  or  IJ  inches. 


First-driving  wheel,  27  teeth. 

Diameter  of  back  roller,  8,  or  1  inch. 
3  X  2=6 

First-driven  wheel,  48  teeth. 

Driving-wheel.  Driven-wheel. 
27  teeth.  48  teeth. 
Back  roller,  1  inch,  or  8  9,  or  1^  inch,  front  roller. 


216       )432(2  draught. 


2)6  total  draught. 
3 

2d  dving.  or  change-whl.,  24  teeth. 
2d  driven-wheel,  72  teeth. 
The  draught  is  required  from  the  following  particulars: — 

Driving-wheels,  27,  and  24.    Driven-wheels,  48,  and  72. 
Diameter  of  back  roller,  1  inch,  and  front  roller,  1^,  or  §  inch. 

Driving-wheels.  Driven-wheels. 
27  teeth.  48  teeth. 
24  teeth.  72  teeth. 


108  96 
54  386 


648  3456 

Diam.  back  rol.,  1  in.,  or  8  9,  or  1 J  inch,  diam.  front  rol. 


5184     )31104(6  draught  required. 
31104 

19 


282    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


Wote. — Speeds,  drauglits,  ^c,  may  be  wrought  with  fewer  figures 
by  the  follotving  method  of  cancelling,  viz.,  place  all  the  driven- 
wheels  and  the  diameter  of  the  front  rollers  as  numerators,  and 
all  the  driving-wheels  and  the  diameter  of  the  back  rollers  as 
denominators  ;  then  proceed  by  dividing  with  any  number  that 
will  divide  both  numerator  and  denominator  without  any  re- 
mainder, and  the  results  of  the  numerators  multiplied  together 
for  a  dividend,  and  the  results  of  the  denominators  for  a  divi- 
sor, and  the  quotient  will  be  the  answer  required. 

If  the  driving-wheels  are  27,  and  24,  and  the  diameter  of  the 
back  roller  1  inch,  and  the  driven-wheels  are  48,  and  72,  and  the 
diameter  of  the  front  roller  1^  inch;  what  will  the  draught  be  ? 

6  3 

48    X   72  X   9      6  or  6  draught. 

27        24       8  1 
9 


If  the  back  roller  be  |  inch,  and  the  front  roller  1  inch  diame- 
ter; what  wheels  will  be  required  to  produce  a  draught  of  5J? 

Diameter  of  front  roller,  8,  or  1  inch. 

3 

First  driving-wheel  24  teeth. 

Diameter  of  the  back  roller  7,  or  |  inch. 
3  X  2=6 

First  driven-wheel,  42  teeth. 

Driving-wheel.  Driven-wheel. 
24  teeth.   42  teeth. 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  front  roller. 


168         )336(2  draught. 
336 


1 


\ 


WHEELS  EEQUIKBD  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  283 

2)5.5  total  draught. 


.  2.75 

2d  driving,  or  change-wheel,  28  teeth. 


2200 
550 


2d  driven-wheel  77.00  teeth. 

If  the  driving-wheels  be  24,  and  28,  the  diameter  of  the  back 
roller  |  inch,  and  the  driven-wheels  42,  and  77,  and  the  diame- 
ter of  the  front  roller  1  inch,  what  will  the  draught  be  ? 

Driving-wheels.  Driven-wheels. 
24  teeth.  '  42  teeth. 
28  teeth.    77  teeth. 


192  294 
48  294 


672  3234 
Back  roller,  I  inch,  or  7  8,  or  1  inch,  front  roller. 


4704      )2o872(5.5,  or  5i  draught. 
■  23520 


23520 
23520 


If  the  back  roller  be  |  inch,  and  the  front  roller  1  inch  diame- 
ter; what  wheels  will  be  required  to  produce  a  draught  of  2 J  in 
the  first  driving  and  driven-wheels,  and  a  total  draught  of  7? 

Diameter  of  front  roller,  8,  or  1  inch. 

3 

First  driving-wheel,  24  teeth. 

Diameter  of  back  roller,  7,  or  |  inch, 
3  X  2  =  6 

42 

Add  21  divided  by  3  =  7 


First  driven-wheel,  49  teeth 


284    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT, 


Driving-'wheel.  Driven-wheel. 
24  teeth.    49  teeth. 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  front  roller. 


168         )392(2i  draught. 
336 


168 

2^  draught.  7,  total  draught. 
3  3 

7  7)21 


3 

■  21  second  driving  or  change-wheel. 
63  second  driven-wheel. 

If  the  driving-wheels  be  24,  and  21,  and  the  driven-wheels  49, 
and  63,  the  back  roller  |  inch,  and  the  front  roller  1  inch  diame- 
ter ;  what  will  the  draught  be  ? 

Driving-wheels.  Driven-wheels. 
24  teeth.    49  teeth. 
21  teeth.    63  teeth. 

24  147 
48  294 


504  3087 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  front  roller. 

3528      )24696(7  draught. 
24696 

If  the  diameter  of  the  front  roller  be  IJ  inch,  and  the  back 
roller  1  inch ;  what  wheels  will  be  required  to  produce  a  draught 
of  41? 

Diameter  of  the  front  roller,  9,  or  IJ  inch. 

2 

First  driving-wheel  18  teeth. 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  285 


Diameter  of  back  roller,  8,  or  1  incli. 
2  X  2=4 

First  driven-wheel,  32  teeth. 

Driving-wheel.  Driven-wheel. 
18  teeth.    32  teeth. 
Back  roller,  1  inch,  or  8  9,  or  IJ  inch,  front  roller. 


144         )288(2  draught. 
288 

2)4.5  total  draught. 
2.25 

2d  driving-wheel,  28  teeth. 


2d  driven- wheel,  63  teeth. 

The  draught  in  rollers  is  required,  when  the  driving-wheels  are 
18,  and  28,  and  the  driven  wheels  32,  and  63,  and  the  diameter 
of  the  back  roller  1  inch,  and  front  roller  inch. 


1800 
450 


Driving-wheels.  Driven-wheels. 


18  teeth.  32  teeth. 
28  63 


144 
36 


96 
192 


504 


2016 


Back  roller,  1  inch,  or  8 


9,  or  IJ  inch  front  roller. 


4032      )18144(4.5,  or  4i  draught. 
16128 


20160 
20160 


286    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


What  wheels  will  be  required  to  produce  7J  draught,  if  the 
back  roller  be  1  inch  diameter,  and  the  front  roller  1|  inch? 

Diameter  of  front  roller,      inch,  =  9 


First  driving-wheel,  27  teeth. 

Diameter  of  back  roller,  1  inch,  or  8 

3  X  2=6 

48 

Add  24  divided  by  2  for  one-half =12 

First  driven-wheel,  60  teeth. 

Driving-wheel.  Driven-wheel. 
27  teeth.  60  teeth. 
Diam.  of  back  rol.  1  in.,  or  8  9,  or  1|  in.  diam.  of  front  rol. 


216        )540(2.5,  or  2i  draught. 
432 


1080 
1080 

7J  is  the  total  draught  required,  which  must  be  divided  by  2J 
the  first  draught ;  the  quotient  of  which  multiplied  by  the  second 
driving  or  change-wheel,  will  give  the  second  driven-wheel. 

Thus, 

2.5)7.5(3  multiplied  by  wheel  26  teeth,  will 
75  be  equal  to  78  teeth,  wheel  2d 
—  driven. 

The  draught  in  rollers,  is  required  from  the  following  particu- 
lars:— 

Driving-wheels,  27,  and  26  teeth.  Driven-wheels,  60,  and  78  tth. 
Back  roller,  1  inch  diameter;  and  front  roller,  1|  inch. 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  287 

Driving-wheels.  Driven-wheels. 
27  teeth.  60  teeth. 

26  teeth.  78  teeth. 


162  4680 

54  9,  or      inch,  front  rol. 


702  42120  dividend. 

Bk.  rol.  1  in.,  or  8 


5616  divisor. 

5616)42120(7.5,  or  7i  draught 
39312 


28080 
28080 


Or, 

BY  CANCELLING- 

15  3 

m     78      9  15 

—  —  —  =  —  =  7|  draught- 
27     26       8  2 


9 


If  the  diameter  of  the  front  roller  be  1  inch,  and  the  back 
roller  |  inch ;  what  wheels  will  be  req^uired  to  produce  a  draught 
of  8  ? 

Diameter  of  front  roller,  1  inch,  or  8 

3 

First  driving-wheel,  24  teeth. 

Diameter  of  back  roller,  |  inch,  or  7 

3  X  2  =  6 

First  driven-wheel,  42  teeth. 


288    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


Driving-wheel.  Driven-wlieel. 
24  teeth.  42  teeth. 
Back  roller,  ^  inch,  or  7  8,  or  1  inch,  front  roller. 


168        )336(2d  draught. 
336 

2)8  total  draught. 
4 

2d  driving-Trheel,  20  teeth. 

2d  driven-wheel,  80  teeth. 

If  the  driving-wheels  be  24,  and  30,  and  the  driven-wheels  42, 
and  80,  the  back  roller  |  inch  diameter,  and  the  front  roller  1 
inch  J  what  will  the  draught  be? 

Driving-wheels.  Driven-wheels. 
24  teeth.  42  teeth. 
20  teeth.  80  teeth. 


480  3360 

Diam.  of  bk.  rol.,  |  in.,or  7  8,  or  1  in.  diam.  of  front  rol. 


3360     )26880(8  draught  at  rollers. 
26880 

If  the  diameter  of  the  back  roller  be  |  inch,  and  the  front 
roller  1  inch ;  what  wheels  will  be  required  to  produce  a  draught 
of  9,  i.  e.,  1  into  9? 

Diameter  of  front  roller,  8,  or  1  inch. 

3 

1st  driving-wheel,  24  teeth. 

Diameter  of  back  roller,  7,  or  |  inch. 
3  X  2  =  6 

42 

Add  21  divided  by  3=7 

1st  driven-wheel,  49  teeth. 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  289 

Driving-wheel.  Driven-wlieel. 
24  teeth.    49  teeth. 
Back  rollers,  |  inch,  or  7  8,  or  1  inch  front  roller. 


168         )392(2i  draught. 
336 


56 
 1 

—  3" 

168 

2J  draught  9  total  draught. 

3  8 

7  7)27 

2d  driving-wheel,  21  teeth. 

2d  driven-wheel,  81  teeth. 

The  draught  in  rollers,  is  required  from  the  following  par- 
ticulars : — 

Driving-wheels,  24,  and  21  teeth.  Diameter  of  back  roller,  |  inch. 
Driven-wheels,  49,  and  81  teeth.  Diameter  of  front  roller,  1  inch. 

Driving-wheels.  Driven-wheels. 
24  teeth.    49  teeth. 
21  teeth.    81  teeth. 

24  49 
48  392 


504  3969 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  front  roller. 


3528      )31752(9  draught. 
31752 


290    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 

If  the  diameter  of  the  back  roller  be  1  inch,  and  the  front 
roller  1|  inch,  what  wheels  will  be  required  to  produce  a  draught 
of  2J,  between  the  first  driving  and  driven-wheels,  and  a  total 
draught  of  8.4375? 

Diameter  of  front  roller,  9,  or  1|  inch. 

3 

1st  driving-wheel,  27  teeth. 

Diameter  of  back  roller,  8,  or  1  inch. 
3  X  2  =  6 

48 

Add  24  divided  by  4  =  6 

1st  driven-wheel,  54  teeth. 

Driving-wheels.  Driven-wheels. 
27  teeth.  54  teeth. 
Diam.  back  rol.,  1  in.,  =  8  9,  or  IJ  inch,  front  roller. 


Divisor  216         486  dividend. 

216)486(2.25,  or  2i  draught,  between  the  first 
432  driving  and  driven-wheels. 


540 
432 


1080 
1080 

Draught  required. 
1st  draught,  2.25)8.4375(3.75  =  2d  draught. 
675 


1687 
1575 


1125 
1125 


WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  291 

3.75,  2d  draught. 
2d  driving,  or  change-wheel,  24  teeth. 


1500 
750 


90.00  2d  driven  wheel,  90  teeth. 

The  draught  in  rollers  is  required  from  the  following  particu- 
lars:— 

Driving-wheels,  27,  and  24  teeth.  Diameter  of  back  roller,  1  inch. 
Driven-wheels  54,  and  90  teeth.  Diameter  of  front  roller  1 J  inch. 

Driving-wheels.  Driven-wheels. 
27  teeth.    54  teeth. 
24  teeth.     90  teeth. 


108  4860 

54  9,  or  IJ  inch,  front  roller. 


648         43740  dividend. 
Back  rollers,  1  inch,  or  8 


5184  divisor. 

5184)43740(8.4375  draught  required. 
41472 


22680 
20736 


19440 
15552 


38880 
36288 


25920 
25920 

If  5J  hank  roving  produces  No.  45's  twist,  what  will  the  total 
draught  at  the  mules  be  ? 


292    WHEELS  REQUIRED  TO  PRODUCE  ANY  GIVEN  DRAUGHT. 


Hank  roving,        45's  No.  of  twist. 
3  3 


16  )135(8.4375  draught  required  at  the 
128  mules. 


70 

64  120 

  112 

60   

48  80 
  80 

N.  B. —  When  there  are  any  fractional  parts  in  the  divisor,  or 
dividend,  reduce  them  to  the  same  name  as  in  the  last  example. 

•If  the  diameter  of  the  back  roller  be  |  inch,  and  the  front 
roller  1  inch,  what  wheels  will  be  required  to  produce  a  draught 
of  lOf,  or  10,666;  the  draught  between  the  first  driving  and 
driven-wheels  to  be  2f ,  or  2.666. 

Diam.  of  front  rol.,  1  inch,  or  8.    Diam.  of  bk.  rol.  |  inch,  or  7 

3  3x2=6 

1st  driving-wheel,  24  teeth.  42 

Add  f  of  21  =  14 

1st  driven-wheel,  56  tth. 

Driving-wheel.  Driven-wheel. 
24  teeth.    56  teeth. 
Back  roller  |  inch,  or  7  8,  or  1  inch  front  roller. 


168  )448(2.66,  first  draught. 

336 


1120 
1008 


1120 
1008 


112 


WHEELS  EEQUIKED  TO  PRODUCE  ANY  GIVEN  DRAUGHT.  293 


Draught  required. 
1st  draught,  2.66)10.66(4,  2d  draught. 
1066 

2d  driving,  or  change-wheel,  22  teeth. 

4,  2d  draught. 

2d  driven-wheel,  88  teeth. 

The  draught  between  the  back  and  front  rollers  of  a  throstle, 
is  required  from  the  following  particulars : — 

Driving-wheels,  24,  and  22  teeth. 
Driven-wheels,  56,  and  88  teeth. 
Diameter  of  back  roller,  |  inch. 
Diameter  of  front  roller,  1  inch. 

Driving-wheels.  Driven-wheels. 
24  teeth.    56  teeth. 
22  teeth.    88  teeth. 


48  448 

48  448 

528  4928 
Back  roller,  |  inch,  or  7  8,  or  1  inch,  front  roller. 


3696    ^  )39424(10.66,  or  lOf,  draught  be- 
*   3696  tween  back  and  froni 

 ■  rollers  of  the  throstle, 

24640 
22176 


24640 
22176 


2464 


EXPLANATION  TO  THE  REED  TABLE. 

1.  Manchester  and  Stockport  count  by  the  number  of  ends  in 

1  inch. 

2.  Bolton  counts  by  the  number  of  beers  on  24^  inches,  20 

dents  to  a  beer. 

3.  Blackburn  counts  by  the  number  of  beers  on  45  inches,  20 

dents  to  a  beer. 


294 


EXPLANATION  TO  THE  KEED  TABLE. 


4.  6-4ths  Preston  counts  by  the  number  of  beers  on  58  inches? 

20  dents  to  a  beer. 

5.  9-8ths  Preston  counts  by  the  number  of  beers  on  44  inches, 

20  dents  to  a  beer. 

6.  4-4ths  Preston  counts  by  the  number  of  beers  on  39  inches, 

20  dents  to  a  beer. 

7.  7-8ths  Preston  counts  by  the  number  of  beers  on  34  inches, 

20  dents  to  a  beer. 

8.  Nankeen  counts  by  the  number  of  beers  on  20  inches,  19 

dents  to  a  beer. 

9.  Scotch  and  Carlisle  count  by  the  number  of  dents  on  37 

inches. 

10.  Silk  counts  by  the  number  of  ends  on  36  inches. 

11.  Number  of  dents  in  1  yard. 

12.  The  United  States  of  America,  the  number  of  splits  or  dents 

in  a  reed  36  inches  wide,  indicates  the  count  of  cloth  in 
the  States  of  Pennsylvania,  New  Jersey  and  Delaware, 
and  throughout  nearly  all  the  States  for  all  twilled  goods, 
but  plain  goods  are  counted  by  the  number  of  threads  on 
an  inch,  each  split  or  dent  containing  2  threads.  For 
instance, 

If  we  wish  to  determine  the  count  of  any  particular 
plain  goods,  we  count  the  number  of  threads  on  an  inch, 
and  that  number  multiplied  by  36,  and  divided  by  2,  gives 
you  the  reed  on  which  the  goods  were  woven. 

In  setting  print  cloths,  the  number  of  threads  on  an 
inch  are  taken  as  the  count,  via.  If  you  have  cloth  woven 
in  a  1200  reed,  you  multiply  the  count  of  the  reed  by  2, 
which  will  make  2400,  and  that  divided  by  36  will  be  66, 
which  will  designate  the  count  of  that  particular  kind 
of  goods.  Throughout  New  England  generally,  the  above 
count  is  used  for  all  plain  goods,  and  the  number  of  dents 
in  a  reed  for  twilled. 

The  first  line  in  each  division  is  the  number  of  dents  in  1  inch  ; 
opposite  to  which  is  the  count  of  the  reed,  according  to  the  sys- 
tem of  counting. 

iV.  B. — A  dent  is  generally  called  a  split  in  Scotland  ;  a  beer  is 
generally  called  a  porter  in  Scotland. 

Bleached  or  finished  goods  generally  decrease  in  width  about 
10  per  cent. 


REED  TABLE. 


295 


REED  TABLE, 


2 

3 

4 

5 

United  States. 

Bolton. 

Blackburn. 

6-4ths. 
Preston. 

9-8tlis. 
Preston. 

N.  of 

count 

N.  of 

count 

N.  of 

count 

N.  of 

count 

N.  of 

count 

dts.  in 

of 

dts.  in 

of 

dts.  in 

of 

dts.  in 

of 

dts.  in 

of 

1  in. 

reed. 

1     i  n 

1  in. 

reed . 

1  in. 

reed. 

1     >  n 

I  in. 

reed. 

1  in. 

reed. 

1  "S 

ou 

1  '\ 
k  o 

1  S  1  87 

1  o 

7'S 

1 

43.5 

15 

O.J. 

1  B 

1  6 

19.4 

1  fi 

O  V/. 

1 6 

46  4 

1  fi 

Ti  9 

1  7 

^4 

1  7 

20.612 

1  7 

38.25 

1  7 

49.3 

1  7 

^7  4 

1  H 

^fi 

1  8 

21.825 

1  H 

40 

lO 

18 

52.2 

1  R 

O.7.  U 

19 

oo 

19 

23.037 

19 

42  75 

19 

55.1 

1  Q 

1  i7 

41  ft 

^u 

24  9'^ 

90 

4 

90 

'58 

90 

44 

21 

4.2 

21 

25.462 

21 

47  9 

2 1 

60.9 

91 

4fi  9 

22 

44 

22 

26.675 

22 

49.5 

22 

63.8 

99 

4ft  4 

1 

4fi 
^  yj 

23 

27  RS7 

4  .00/ 

9^ 

1  7'i 

2*1 

66.7 

9^ 

1^0  fi 

I  24 

24 

29.1 

24 

54. 

24 

69.6 

94 

ft 

1  25 

50 

25 

30.31 

25 

56.25 

25 

72.5 

9^ 

o  o . 

2fi 

31.52 

2fi 

58.5 

26 

75.4 

9fi 

^17  9 

27 

54 

27 

32.73 

27 

60.75 

27 

78.3 

27 

59.4 

28 

56 

28 

33.95 

28 

63. 

28 

81.2 

28 

61.6 

29 

58 

29 

35.16 

29 

65.25 

29 

84.1 

29 

63.8 

30 

60 

30 

36.87 

30 

67.5 

30 

87. 

30 

66. 

^1 

62 

31 

37.58 

31 

69.75 

31 

89.9 

31 

68.2 

32 

64 

32 

38.8 

32 

72. 

32 

92.8 

32 

70.4 

33 

66 

33 

40.1 

33 

74.25 

33 

95.7 

33 

72  6 

34 

68 

34 

41.22 

34 

76.5 

34 

98.6 

34 

74.8 

35 

70 

35 

42.43 

35 

78.75 

35 

101.5 

35 

77. 

36 

72 

36 

43.65 

36 

81. 

36 

104.4 

36 

79.2 

37 

74 

37 

44.86 

37 

83.25 

37 

107.3 

37 

81.4 

38 

76 

38 

46.07 

38 

85.5 

38 

110.2 

38 

83.6 

39 

78 

39 

47.28 

39 

87.75 

39 

J13.1 

39 

85.8 

40 

80 

40 

48.5 

40 

90. 

40 

116. 

40 

88, 

41 

82 

41 

49.71 

41 

92.25 

41 

118.9 

41 

90.2 

! 

84 

42 

50.9 

42 

94.5 

42 

121.8 

42 

92.4 

43 

86 

43 

52.13 

43 

96.75 

43 

124.7 

43 

94.6 

44 

88 

44 

53.35 

44 

99. 

44 

127.6 

44 

96.8 

296 


REED  TABLE. 


REED  TABLE. 


6 

7 

8 

9 

10 

It 

4*4ths 

i:^r6ston . 

7-8ths.  Preston. 

Nankeen. 

Scotch. 

Silk. 

N.  of 

count 

N .  of 

count 

IN .  01 

COU  lit 

N.  oi 

count 

N.  of 

COUHt 

N.  of 

dta. in 

OI 

dts. in 

of 

dts. in 

of 

dts.  in 

of 

d  ts. in 

of 

dts.  in 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  yard. 

15 

29.25 

;5 

25.5 

15 

15.79 

15 

555 

15 

1080 

540 

16 

31.2 

16 

27.2 

16 

16.842 

16 

592 

16 

1152 

576 

17 

33.15 

17 

28.9 

17 

17.894 

17 

629 

17 

1224 

612 

18 

35.1 

18 

30.6 

18 

18.947 

18 

666 

18 

1296 

648 

19 

37.05 

19 

32.3 

19 

20. 

19 

703 

19 

1368 

684 

20 

39. 

20 

34. 

20 

21.052 

20 

740 

20 

1440 

720 

21 

40.95 

21 

35.7 

21 

22.105 

21 

777 

21 

1512 

756 

22 

42.9 

22 

37.4 

22 

23.157 

22 

814 

22 

1584 

792 

23 

44.85 

23 

39.1 

23 

24.21 

23 

851 

23 

1656 

828 

24 

46.8 

24 

40.8 

24 

25.26 

24 

888 

24 

1728 

864 

25 

48.75 

25 

42.5 

25 

26.31 

25 

925 

25 

1800 

900 

26 

50.7 

26 

44.2 

26 

27.36 

26 

962 

26 

1872 

936 

27 

52.65 

27 

45.9 

27 

28.42 

27 

299 

27 

1944 

972 

28 

54.6 

28 

47.6 

28 

29.47 

28 

1036 

28 

2016 

1008 

29 

56.55 

9Q 

1044 

30 

58.5 

30 

51. 

30 

31.57 

30 

1110 

30 

2160 

1080 

31 

00.45 

31 

52.7 

31 

32.63 

31 

1147 

31 

2232 

1116 

32 

62.4 

32 

54.4 

32 

83.68 

32 

1184 

32 

2304 

1152 

33 

64.35 

33 

56.1 

33 

34.73 

33 

1221 

33 

2376 

1188 

34 

66.3 

34 

57.8 

34 

35.79 

34 

1258 

34 

2448 

1224 

35 

68.25 

35 

59.5 

35 

36.84 

35 

1295 

35 

2520 

1260 

36 

70.2 

36 

61.2 

36 

37.89 

36 

1332 

36 

2592 

1296 

37 

72.15 

37 

62.9 

37 

38.94 

37 

1369 

37 

2064 

1332 

38 

74.1 

38 

64.6 

38 

40. 

38 

1406 

38 

2736 

1368 

39 

76.05 

39 

66.3 

39 

41.05 

39 

1443 

39 

2808 

1404 

40 

78. 

40 

68. 

40 

42.1 

40 

1480 

40 

2880 

1440 

41 

79.95 

41 

69.7 

41 

43.15 

41 

1517 

41 

2952 

1476 

42 

81.9 

42 

71.4 

42 

4421 

42 

1554 

42 

3024 

1512 

43 

83.85 

43 

73.1 

43 

45.26 

43 

1591 

43 

3096 

1548 

44 

85.8 

44 

74.8 

44 

46.31 

44 

1628 

44 

3168 

1584 

COUNTING  REEDS.  297 


THE  DIFFERENT  SYSTEMS  OF  COUNTING  REEDS. 
If  there  be  2X  dents  in  an  inch ;  what  count  of  reed  will  it  be 
in  Manchester  or  Stockport? 

21  dents  in  an  inch. 
2  ends  in  a  dent. 

42  count  of  reed. 

If  there  be  26  dents  in  an  inch,  what  count  of  reed  will  it  be 
in  Bolton,  allowing  20  dents  to  a  beer. 

24.25  inches. 

26  dents  in  an  inch. 


14550 
4850 


Dents  in  a  beer,  2.0)63.0.50 

31.525  count  of  reed. 

If  there  be  26  dents  in  an  inch,  what  count  of  reed  will  it  be 
in  Bolton,  allowing  19  dents  to  a  beer  ? 

24.25  inches. 

26  dents  in  an  inch. 


14550 
4850 


Dents  in  a  beer,  19)630.50(33.1842  count  of  reed. 

5T 


60 
57 

  80 

35  76 

19   

  40 

160  38 

152  — 


20 


298  COUNTING  REEDS. 

Suppose  a  reed  contains  33  dents  in  1  inch,  what  count  will 
it  be  according  to  the  different  systems  of  counting? 

UNITED  STATES,  MANCHESTER,  AND  STOCKPORT. 

Multiply  the  number  of  dents  in  1  inch  by  2,  and  the  product 
will  be  the  count  of  the  reed. 

33  number  of  dents  in  1  inch. 
2  ends  in  a  dent. 

66  count  "of  reed. 

BOLTON  COUNT,  20  DENTS  TO  A  BEER. 

Multiply  24J  by  the  number  of  dents  in  1  inch,  and  divide  by 
20,  and  the  quotient  will  be  the  count  of  the  reed. 

24.25  inches. 

33  number  of  dents  in  1  inch. 


7275 
7275 


Number  of  dents  in  a  beer,  2.0)80.0.25 


40.0125  count  of  reed. 

BOLTON  COUNT,  19  DENTS  TO  A  BEER. 

Multiply  24J  by  the  number  of  dents  in  1  inch,  and  divide  by 
19,  and  the  quotient  will  be  the  count  of  the  reed. 

24.25  inches. 

33  dents  in  1  inch. 


7275 
7275 


Dents  in  a  beer,  19)800.25(42.12  count  of  reed. 
76 


40 

38 


22 

19  35 
  38 — nearly. 

N.B. — Some  hinds  of  goods  manufactured  in  Bolton,  reckon  19 
dents  to  a  beer. 


REED  TABLE. 


299 


REED  TABLE. 


1 

2 

3 

4 

United  States. 

Bolton. 

Blackburn. 

6-4th3 
Preston. 

6-4ths 
Preston. 

N.  of 

count 

N.  of 

coutit 

N.  of 

count 

N.  of 

count 

N.  of 

count 

dts.  in 

of 

dts.  in 

of 

dts.  in 

of 

dts.  in 

01 

dts.  in 

of 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

45 

90 

45 

54.56 

45 

101.25 

45 

130.5 

45 

99. 

46 

92 

46 

55.71 

46 

103.5 

46 

133.4 

46 

101.2 

47 

94 

47 

56.98 

47 

105.75 

47 

136.3 

47 

103.4 

48 

96 

48 

58.2 

48 

108. 

48 

139.2 

48 

105.6 

49 

98 

49 

59.41 

49 

110.25 

49 

142.1 

49 

107.8 

50 

100 

50 

60.62 

50 

112.5 

50 

145, 

50 

110. 

51 

102 

51 

61.83 

51 

114.75 

51 

148.9 

51 

112.2 

52 

104 

52 

63.04 

52 

117. 

52 

151.8 

52 

114.4 

53 

106 

53 

64.25 

53 

119.25 

53 

154.7 

53 

116.6 

54 

108 

54 

65.46 

54 

121.5 

54 

157.6 

54 

118.8 

55 

no 

55 

66.687 

55 

123.75 

55 

159.5 

55 

121. 

56 

112 

56 

67.9 

56 

126. 

56 

162.4 

56 

123.2 

57 

114 

57 

69.112 

57 

128.25 

57 

165.3 

57 

125.4 

58 

116 

58 

70.325 

58 

130.5 

58 

168.2 

58 

127.6 

59 

118 

59 

71.537 

59 

132.75 

59 

171.1 

59 

129.8 

60 

120 

60 

72.75 

60 

135. 

60 

174. 

60 

132. 

61 

122 

61 

73  962 

61 

137.25 

61 

176.9 

61 

134.2 

62 

124 

62 

75.175 

62 

139.5 

62 

179.8 

62 

136.4 

63 

126 

63 

76.387 

63 

141.75 

63 

182.7 

63 

138.6 

64 

128 

64 

77.6 

64 

144. 

64 

185.6 

64 

140.8 

65 

130 

65 

78.812 

65 

140.25 

65 

188.5 

65 

143. 

66 

132 

66 

80.025 

66 

148.5 

66 

191.4 

66 

145.2 

67 

134 

67 

81.237 

67 

150.75 

67 

194.3 

67 

147.4 

68 

136 

68 

82.45 

68 

153. 

68 

197.2 

68 

149.6 

69 

138 

69 

83.662 

69 

155.25 

69 

200  1 

69 

151.8 

70 

140 

70 

84.875 

70 

157.5 

70 

203. 

70 

154. 

71 

142 

71 

86.087 

71 

159.75 

71 

205.9 

71 

156.2 

72 

144 

72 

87.3 

72 

1'62. 

72 

208.8 

72 

158.4 

73 

146 

73 

88.512 

73 

164.25 

73 

211.7 

73 

160.6 

74 

148 

74 

89.725 

74 

166.5 

74 

214.6 

74 

162.8 

300 


KEED  TABLE. 


REED  TABLE. 


6 

7 

8 

9 

10 

1  1 

1  1 

4-4th3 
Preston. 

7-Sths 
Preston. 

Nan]<een. 

Scotch. 

Silk. 

N.of 

count 

N.  of 

count 

N.  of 

count 

N.of 

count 

N.  of 

count 

N.  of 

dts.  in 

of 

dts.  in 

of 

dts. in 

of 

dts.  in 

of 

dts.  in 

of 

dts.  in 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  in. 

reed. 

1  yd. 

rtt) 

87  7!^ 

4  Pi 

7fi  f\ 

4 

47  1R 

4 

40 

i  000 

Af\ 

Q94n 

1620 

ftQ  7 

4fi 

7S  9 

^  D 

48  49 

A  (K 
4  D 

1  709 

4R 

1656 

47 

Q  1  fifi 

i7  1  .  Ut> 

47 

7Q  Q 

47 

4Q  47 

47 

1  71Q 

47 
1  / 

1184 

1692 

4R 

4S 

O  1 .  u 

48 

f»n  fi9 

A  8 

1  77R 

48 

14'iR 
O40D 

1728 

49 

4Q 

oo.o 

4Q 

'i  1  Ii7 

4Q 

1811 
I  o  1  o 

4Q 
^y 

•JKOQ 

0040 

1764 

ou 

Q7 

81^ 

fin 

^19  fil 

Ou 

1  oOU 

fin 
ou 

iRnn 

1800 

.J  X 

QQ  4^ 

8fi  7 

fS'^  fi7 

Fa  I 

1  887 
loo/ 

^  1 

1R79 
oO/ ^ 

1836 

O  it 

1  n  1  4 

88  4 

"19 

f^i.  79 

0^ 

1  Q94 

'i9 

1744 

1872 

1 

ill 

'S'l  78 
t>0.  /  o 

fSQ 
Oo 

1  QR  1 

1  y  o  1 

oo 

18  1  R 

1908 

1  O^i  9 
J  V    .  o 

54 

Q1  8 

'S4 

fifi  84 

P>4 

1  QQ8 

fi4 

1888 

1944 

55 

107.25 

55 

Q1 

fi7  8Q4 

oo 

»jy  ou 

1980 

56 

109.2 

56 

el's  9 

ii8  Q47 

OO 

9079 

OD 

4ni9 

2016 

57 

111.15 

57 

96.9 

57 

fin 

^17 

9 1  no 

1^7 
o  / 

4  1  04 

2052 

58 

113.1 

58 

98.6 

58 

61.052 

58 

2146 

58 

4176 

2088 

59 

115.05 

59 

100.3 

59 

62.105 

59 

2183 

59 

4248 

2124 

60 

117. 

60 

102. 

60 

63.158 

60 

2220 

60 

4320 

2160 

61 

118.95 

61 

103.7 

61 

64.21 

61 

2257 

61 

4392 

2196 

62 

120.9 

62 

105.4 

62 

65.263 

62 

2294 

62 

4464 

2232 

63 

122.85 

63 

107.1 

63 

66.316 

63 

2331 

63 

4536 

2268 

64 

124.8 

64 

108.8 

64 

67.368 

64 

2368 

64 

4608 

2304 

65 

126.75 

65 

110.5 

65 

68.421 

65 

2405 

65 

4680 

2340 

66 

128.7 

66 

112.2 

66 

69.473 

66 

2442 

66 

4752 

2376 

67 

130.65 

67 

113.9 

67 

70.526 

67 

2479 

67 

4824 

2412 

68 

132.6 

68 

115.6 

68 

71. .579 

68 

2516 

68 

4896 

2448 

69 

134.55 

69 

117.3 

69 

72.631 

69 

2553 

69 

4968 

2484 

70 

136.5 

70 

119. 

70 

73.684 

70 

2590 

70 

5040 

2520 

71 

138.45 

71 

120.7 

71 

74.737 

71 

2627 

71 

5112 

2556 

72 

140.4 

72 

122.4 

72 

75.789 

72 

2664 

72 

5184 

2592 

73 

142.35 

73 

124.1 

73 

76.842 

73 

2701 

73 

5256 

2628 

74 

144.3 

74 

125.8 

74 

77.894 

74 

2738 

74 

5328 

2664 

COUNTING  REEDS.  301 
BLACKBURN  COUNT,  20  DENTS  TO  A  BEER. 

Multiply  45  by  the  number  of  dents  in  an  inch,  and  divide  by 
the  number  of  dents  in  a  beer,  and  the  quotient  will  be  the  count 
of  the  reed. 

45  inches. 

33  dents  in  an  inch. 


135 
135 


Dents  in  a  beer,  2.0)148.5 


74.25  count  of  reed. 

PRESTON  6-4ths  COUNT,  20  DENTS  TO  A  BEER. 

Multiply  58  by  the  number  of  dents  in  an  inch,  and  divide  by 
20,  and  the  quotient  will  be  the  count  of  the  reed. 

58  inches. 

33  dents  in  an  inch. 


174 
174 


Dents  in  a  beer,  2.0)191.4 


95.7  count  of  reed. 

PRESTON  9-8ths  COUNT,  20  DENTS  TO  A  BEER. 

44  inches. 

38  dents  in  an  inch. 


132 
132 


Dents  in  a  beer,  20)1452(72.6 
140 

52 
40 

120 
120 


302  COUNTING  REEDS. 

N.B. — Some  manufacturers  in  Oldham  count  same  as  Black- 
burn for  fustians  and  velvets ;  printing  cloths  are  same  as 
Manchester. 

PRESTON  4-4ths,  OR  YARD  WIDE  COUNT,  20  DENTS  TO  A  BEER. 

Multiply  39  by  the  number  of  dents  in  an  inch,  and  divide  by 
the  number  of  dents  in  a  beer,  and  the  quotient  will  be  the  count 
of  the  reed. 

39  inches. 

33  dents  in  an  inch. 


117 
117 


Dents  in  a  beer,  2.0)128.7 


64.35  count  of  reed. 

PRESTON  7-8ths  COUNT,  20  DENTS  TO  A  BEER. 

Multiply  34  by  the  number  of  dents  in  an  inch,  and  divide  by 
the  number  of  dents  in  a  beer,  and  the  quotient  will  be  the  count 
of  the  reed. 

34  inches. 

33  dents  in  an  inch. 


102 
102 


Dents  in  a  beer,  2.0)112.2 

56.1  count  of  reed. 

NANKEEN  COUNT,  19  DENTS  TO  A  BEER. 

Multiply  20  by  the  number  of  dents  in  an  inch,  and  divide  by 
the  number  of  dents  in  a  beer,  and  the  quotient  will  be  the  count 
of  the  reed. 

20  inches. 

33  dents  in  an  inch. 


660 


COUNTING  REEDS. 


303 


Dents  in  a  beer,  19)660(84.73,  or  nearly  34|-,  count  of  reed. 
57 


90 
76 


140 
133 


70 
57 


13 


SCOTCH  AND  CARLISLE  COUNT. 

Multiply  37  by  the  number  of  dents  in  an  inch,  and  the  pro- 
duct will  be  the  count  of  the  reed. 

37  inches. 

33  dents  in  an  inch. 


Ill 
111 


1221  count  of  reed. 


SILK  COUNT. 

Multiply  36  by  the  number  of  dents  in  an  inch,  and  that  pro- 
duct by  2,  -which  will  be  the  count  of  the  reed. 

36  inches. 

33  dents  in  an  inch. 


108 
108 


1188 

2  ends  in  a  dent. 


2376  count  of  reed.  > 

NUMBER  OF  DENTS  IN  A  YARD. 

Multiply  the  number  of  dents  in  an  inch  by  the  number  of 
inches  in  a  yard,  and  the  product  will  be  the  number  of  dents  in 
a  yard. 


304 


COUNTING  REEDS. 


33  dents  in  an  inch. 
36  inches  in  a  yard. 

198 
99 


1188  dents  in  a  yard. 

Some  manufacturers  count  calicoes,  checks,  and  handkerchiefs, 
by  the  number  of  beers  in  a  yard,  some  19,  and  some  20  dents 
to  a  beer. 

By"20  dents  to  a  beer. 

36  inches  1  yard. 
33  dents  in  an  inch. 


108 
108 


Dents  in  a  beer,  2.0)118.8 

59.4  count  of  reed. 

By  19  dents  to  a  beer. 

36  inches  1  yard. 
33  dents  in  an  inch. 


108 
108 


Dents  in  a  beer,  19)1188(62.526  count  of  reed. 
114 


48 

38 

100 

95 

120 

50 

114 

38 

6 

COUNTING  REEDS.  305 

Some  manufacturers  of  fustians,  velvets,  velveteens,  velveretts, 
satteens,  &c.,  count  by  the  number  of  beers  set  on  24  inches  at 
the  reed,  some  20,  and  some  19  dents  to  a  beer. 

24  inches. 

33  dents  in  an  inch. 


72 
72 


Dents  in  a  beer,  2.0)79.2 


39. G  count  of  reed.  ' 

If  there  be  33  dents  in  an  inch,  how  many  beers,  19  dents  to 
a  beer,  will  there  be  in  24  inches? 

33  dents  in  an  inch. 
24  inches. 


132 
66 


Dents  in  a  beer,  19)792(41.684  count  of  reed. 
76 


32 
19 


130 
114 


160 
152 


80 
76 


4 

How  many  dents  will  there  be  in  an  inch,  in  a  6-4ths  145 
Preston  reed? 

Multiply  the  count  of  the  reed  by  the  number  of  dents  in  a 


306  MANUPACTURING. 

beer,  and  divide  by  the  number  of  inches  any  given  number  of 
beers  is  set  on,  and  the  quotient  will  be  the  number  of  dents  in 
an  inch. 

145  count  of  reed. 
20  dents  to  a  beer. 


Inches  set  on,  58)2900(50,  number  of  dents  in  an  inch. 
290 


0 

Whatever  the  count  of  the  reed,  or  system  of  counting  may 
be,  by  referring  to  the  table,  you  will  find  the  number  of  dents 
in  an  inch. 

The  number  of  dents  in  an  inch  multiplied  by  2,  and  that 
product  multiplied  by  the  number  of  inches  intended  to  be  filled 
at  the  reed,  will  give  the  number  of  ends  required  in  the  warp, 
for  any  kind  of  plain  goods. 


MANUFACTURING. 

Rules  and  examples  for  ascertaining  the  weight  of  warp  and 
weft,  required  for  the  manufacture  of  any  description  of  cotton 
goods,  according  to  the  length  and  width  of  the  piece,  and  the 
fineness  of  yarns. 

On  account  of  some  kind  of  goods  requiring  to  be  laid  a 
greater  length  on  the  warping  mill  than  others,  it  will  be  found 
the  most  accurate  to  ascertain  the  length  and  weight  of  twist 
required  for  the  warp,  and  divide  by  the  number  of  cuts  or  pieces 
in  the  warp,  which  will  give  the  length  and  weight  of  twist  (ac- 
cording to  its  fineness)  required  for  one  cut,  or  piece  of  cloth. 

N.B. —  The  general  allowance  for  waste,  is  about  l-50iA  of  the 
weight  of  weft  required  to  weave  the  piece. 

TO  ASCERTAIN  THE  WEIGHT  OF  A  WARP. 

RULE. — Multiply  the  length  of  the  warp  by  the  width  in  inches 
required  at  the  reed,  and  that  product  by  the  number  of  ends  in 


MANUFACTURING. 


307 


an  inch,  for  a  dividend.  Then  multiply  the  number  of  yards  in 
one  hank  by  the  number  of  hanks  in  the  pound  of  twist  for  a 
divisor,  and  the  quotient  will  be  the  weight  of  the  warp. 

N.  B. — By  referring  to  the  reed  table,  the  number  of  ends  in  an 
inch  of  any  reed  may  be  found,  according  to  the  system  of 
counting. 

Required,  the  weight  of  number  36's  twist,  for  a  warp  146 
yards  long,  29  inches  wide  at  the  reed,  and  72  ends  in  an  inch? 

146  yards,  length  of  warp. 
29  inches,  width  at  reed. 


1314 
292 


4234 

72  ends  in  an  inch. 


8468 
29638 


Dividend,  304848  yards  of  twist  in  the  warp. 

840  yards,  1  hank. 
36  hanks  in  1  lb. 


5040 
2520 


Divisor,  30240  yards  in  1  lb.  of  36's  twist. 

30240)304848(10  lbs.,  IJ  oz.  weight  of  warp. 
30240 


2448 

16  oz.=l  lb. 


14688 
2448 


39168 


308 


MANUFACTURING. 


30240)39168(1  ounce. 
30240 


8928 

4  qrs.,  1  oz. 


30240)35712(1  qr. 
30240 


5472 

The  -weight  of  warp  or  weft  may  be  found  in  a  much  easier 
way,  by  dividing  the  number  of  yards  of  twist,  or  weft  required, 
by  the  number  of  yards  in  1  ounce,  which  will  be  found  in  the 
yarn  table  according  to  the  fineness  of  the  yarns,  as  in  the  follow- 
ing example: — 

Required,  the  weight  of  36's  twist,  for  a  warp  146  yards  long, 
29  inches  wide  at  the  reed,  and  72  ends  in  an  inch  ? 

146  yards,  length  of  warp. 
29  inches,  width  of  warp  at  reed. 


1314 
292 


4234 

72  ends  in  an  inch. 


8468 
29638 


Dividend,  304848  yards  in  warp. 

Yards  in  1  oz.  of  36's  twist,  1890)304848(1611  oz.,  or  10  lbs., 

1890        1 J  oz.,  wt.  of  warp. 


11584 
11340 


2448 
1890 


558 

4  qrs.,  1  oz. 


MANUFACTURING. 


(  309  '"^ 

1890)2232(1  qr.  ■ , 

1890  ■■^^A'R' 


342 


If  there  be  304848  yards  of  36's  twist,  in  a  warp  containing 
5  cuts  or  pieces;  what  weight  of  twist  will  there  be  in  1  piece? 

Cuts,  or  pieces  in  warp,  5)304848  yards  of  twist  in  warp. 


Yds.  in  1  oz.  of  36's  twist,  1890)60969.6(321  oz.,  or  2  lbs.,  Oi  oz., 

6670         wt.  of  twist  required 

  for  1  piece  of  cloth. 

4269 
3780 


489.6 

4  qrs.,  1  oz. 


1890)1958.4(1  qr. 
1890 


68.4 

Required,  the  weight  of  number  36's  weft,  to  weave  a  piece  of 
cloth  30  yards  long,  29  inches  wide,  and  84  threads,  or  picks  in 
an  inch,  allowing  l-40th  for  waste? 

30  yards,  length  of  piece. 
29  inches,  Avidth  of  piece. 


870 

84  threads  or  picks  in  an  inch. 


3480 
6960 

73080 

Allowance  for  waste,  1-40  1827 


Dividend,  74907  yards  required  to  weave  a  piece. 


1 


310 


MANUFACTURING. 


Yards  in  1  ounce,  1890)74907(391  oz.,  or  2  lbs.,  7J  oz.,  weight  of 


  of  cloth. 

18207 
17010 


1197 

4  qrs.,  1  oz. 


1890)4788(2  qrs. 
3780 


1008 

Or  Tims, 

1  lea  is  12.0  yds.)7490.7  yards  of  weft  required  to  weave  a  piece. 
1  hank,  7  leas)624.225 


6)89.175  hanks,  or  2  lbs.,  7^  oz.,  weight  of 


6)14.8625 


2.477083  lbs. 

16  oz.,  1  lb. 


2862500 
477083 


7.633333  oz. 


2.533333  qrs. 

Or  Thus, 

840  yards,  1  hank. 
86  hanks,  1  lb. 

5040 
2520 

Divisor,  30240  yards  in  1  lb.  of  36 's  weft. 


5670 


weft  required  to  weave  a  piece 


weft  required. 


4 


MANUFACTURING.  311 

30240)74907(2  lbs.  TJ  oz.,  weight  of  weft  required. 
60480 


14427 
16 


86562 
14427 


30240)230832(71 
211680 


19152 

Required,  the  weight  of  number  60's  twist,  for  a  warp  146 
yards  long,  39  inches  wide,  and  106  ends  to  an  inch  ? 

146  yards,  length  of  warp. 
39  inches,  width  at  the  reed. 


1314 
438 


6694 

I  106  ends  in  an  inch. 


34164 
56940 


1  lea,  12.0  yards)60356.4  yards  of  twist  in  warp. 


1  hank  is  7  leas)5029.7  leas  of  twist  in  warp. 


Numbers  of  twist  6.0)71.8.52857  hanks  of  twist  in  warp. 


11.9754761  lbs.  of  twist  in  warp. 
16  ounces,  1  lb. 


58528566 
9754761 


15.6076176  ounces. 

4  qrs.,  1  oz. 


2.4304704  qrs. 


312  MANUFACTURING. 

The  weight  of  twist  required  for  the  warp,  is  11  lbs.,  15J  oz. 

If  there  be  603564  yards  of  number  60's  twist  in  a  warp; 
what  will  it  weigh  ? 

Yards  in  1  ounce  of  60's  twist,  3150)603564(191J  ounces,  or  11 

3150  pounds,  15J  oz., 

  weight  of  warp. 

28856 
28350 


5064 
3150 


1914 

4  qrs.,  1  oz. 


3150)7656(2  qrs. 
6300 


1356 

If  a  warp,  146  yards  long,  39  inches  wide,  and  106  ends  in  an 
inch,  weigh  12  lbs.,  what  numbers  of  twist  will  it  be  ? 

146  yards,  length  of  warp. 
89  inches,  width  of  warp  at  reed. 


1314 

438 


5694 

106  ends  in  an  inch. 

34164 
56940 


Wt.  of  warp  12  lbs.)603564  number  of  yards  in  a  warp. 
50297 


MANUFACTDRmG. 


313 


1  hank  is  840  yards)50297(59.87  nearly,  number  OO's  twist. 
4200 


8297 
7560 


7370 
6720 


6500 
5880 


620 

What  length  and  weight  of  number  SO's  weft,  will  it  require  to 
weave  a  warp  146  yards  long,  39  inches  wide  at  the  reed,  and 
120  threads,  or  picks  in  an  inch,  allowing  l-50th  for  waste  ? 

146  yards,  length  of  warp. 
120  threads,  or  picks  in  an  inch. 


17520 

39  inches,  width  at  reed. 


157680 
52560 


683280 

Add  l-50th  for  waste  13665.6 


696945.6  yards  required  to  weave  the  warp. 
1  lea  is  12.0  yds.)69694.5.6  yds.  of  weft  required  to  weave  a  piece. 


1  hank  is  7  leas.)5807.88  leas  of  do. 


829.69714  hanks. 

7  leas,  1  hank. 


4.87998  leas. 

120  yards,  1  lea. 


105.59760  yards. 

21 


314  MANUFACTURING. 

The  length  of  weft  required  to  weave  the  warp  will  be  829 
hanks,  4  leas,  and  105|  yards. 

Numbers  of  weft,  8.0)82.9.69714  hanks  of  BO's  weft. 


10.371214  lbs. 

16  ounces,  1  lb. 


2227284 
371214 


5.939424  oz. 

4  qrs.,  1  oz. 


3.757696  qrs. 

10  lbs.  5f  oz.,  nearly  10  lbs.,  6  oz.  weight  of  SO's  weft,  required 
to  weave  the  warp. 

What  length  and  weight  of  number  60's  twist,  will  it  require 
for  a  piece  of  cloth  29i  yards  long,  39  inches  wide,  and  106 
ends  in  an  inch  ? 

29.2  yards,  length  of  piece. 
39  inches,  width  at  reed. 


2628 
876 


1138.8 

106  ends  to  an  inch. 


68328 
113880 


Dividend,  120712.8  yards  of  twist  required  for  a  piece. 

840  yards,  1  hank. 
60's  twist. 


Divisor,  50400  yards  in  1  lb.  of  number  60's  twist. 


MANUFACTURING. 


315 


50400)120712.8(2  lbs.,  6}  oz.,  weight  of  twist  re- 
100800  quired  for  1  piece  of  cloth. 


19912.8 

16  ounces,  1  lb. 


1194768 
199128 


50400)318604.8(6  ounces. 
302400 


16204.8 

4  qrs.,  1  oz. 


50400)64819.2(1  qr. 
50400 


14419 

The  weight  of  number  60's  twist  required  for  1  piece  of  cloth, 
is  2  lbs.,  6|-  oz.,  or  11  lbs.,  15J  ounces,  for  1  warp  containing 
5  pieces. 

What  weight  of  number  80's  weft,  will  it  require  to  weave  1 
piece  of  cloth  29i  yards  long,  120  picks,  or  threads  in  an  inch, 
and  39  inches  wide,  allowing  l-50th  for  waste  ? 

840  yards  1  hank. 
80's  weft. 


67200  divisor. 

29.2  yards,  length  of  piece. 
120  picks,  or  threads  in  an  inch. 


3504.0 

39  inches,  width  at  reed. 


315360 
105120 


136656.0 
Add  l-50th  for  waste  273312 


316  MANUFACTURING. 

Yds.  in  1  lb.,  67200)139389,12(2  lbs.,  l-5th  oz,,  weight  of  weft 
134400     required  to  weave  a  piece  of  cloth. 


4989.12 
16 


2993472 
498912 


67200)79825.92(1  ounce. 
67200 


12625  =  l-5th. 

What  number  of  ends  will  it  require  in  a  warp,  to  fill  50  inches 
in  a  96  reed,  Manchester  count? 

96,  count  of  reed. 
50  inches,  width  at  reed. 

4800,  number  of  ends  required  in  warp. 

What  number  of  ends  will  it  require  in  a  warp,  to  fill  40J 
inches  in  a  118  Manchester  count? 

118,  count  of  Manchester  reed. 
40.5  inches,  width  at  reed. 


590 
4720 


4779.0  number  of  ends  in  warp. 

What  number  of  ends  will  it  require  to  fill  50  inches  in  a  60 
reed,  Bolton  count,  20  dents,  or  40  ends  to  the  beer  ? 

60  reed,  Bolton  count. 
40  ends,  or  20  dents  in  1  beer. 


2400 

50  inches,  width  at  reed. 


120000 


MANUFACTURING. 


31T 


24J  inches,  or  24.25)120000.00(4948  ends  required  in  the  warp. 
9700 


23000 
21825 


11750 
9700 


20500 
19400 


1100 

N.  B. — It  is  not  requisite  to  carry  out  the  decimal  fractions  of 
an  end. 

For  the  different  systems  of  counting  reeds,  see  the  reed  table, 
with  rules  and  examples. 

What  number  of  ends  will  be  required  in  a  warp,  to  fill  51 
inches,  in  a  66  reed,  Bolton  count  ? 

66  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


2640 

51  inches,  width  at  reed. 


2640 
13200 


134640  dividend. 

24J,  or  24.25  inches. )134640(5552  ends  required  for  warp. 
12125 


13390 
12125 


12650 
12125 


5250 
.  4850 


400 


318  MANUrACTURING. 

What  number  of  ends  -will  it  require  in  a  warp,  to  fill  30| 
inches  in  a  7-1  reed,  Blackburn  count? 

74  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


2960 

30.5  inches,  width  of  warp  at  the  reed. 

14800 
88800 


Beers  set  on  45  inches. )90280. 0(2006  ends  required  for  warp. 
90 


280 
270 


10 

What  width  will  2006  ends  fill,  in  a  74  reed,  Blackburn  count  ? 
74,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 

2960  divisor. 
Number  of  ends  in  warp,  2006 

45  inches,  number  of  beers  set  on. 


10030 
8024 


90270  dividend. 

90270  dividend  by  2960=30.5,  or  30i  in.  nearly,  width  of  warp 
at  reed. 

What  number  of  ends  will  it  require  in  a  warp,  to  fill  49^ 
inches,  in  a  135  reed,  Blackburn  count? 


MANUFACTURING. 


319 


135,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


49.5  inches,  width  of  warp  at  the  reed. 


5940  ends  required  in  the  warp. 


What  number  of  inches  will  5940  ends  fill,  in  a  185  reed, 
Blackburn  count  ? 


185,  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


5400  divisor. 

5940  ends  in  the  warp. 

45  inches,  number  of  beers  set  on  reed. 


29700 
23760 


5400)267300(49.5,  or  49J  inches,  width  of  warp  at 


6400 


27000 
48600 
21600 


45  inches,  or 


21600 


the  reed. 


51300 
48600 


27000 
27000 


What  number  of  ends  must  there  be  in  a  warp,  to  fill  48  inches 
in  a  Bolton  54  reed ;  allowing  onlj  19  dents,  or  38  ends  to  a 
beer? 


320 


MANUFACTURING. 


54,  count  of  reed. 

38  ends,  or  19  dents  to  a  beer. 


432 
162 


2052 


48  inches,  "width  of  warp  at  the  reed. 


24.25)98496.00(4062  ends  required  in  the  warp. 


What  number  of  inches  will  4062  ends  fill  in  a  Bolton  54 
reed ;  allowing  19  dents,  or  38  ends  to  a  beer  ? 

64,  count  of  reed. 

38  ends,  or  19  dents  to  a  beer. 


432 
162 


2052  divisor. 


4062  ends  in  the  warp. 
24.25  inches,  numbers  of  beer  set  on. 


20310 
8124 

16248 

8124 


2052)98503.50(48  inches,  width  filled  at  the  reed. 

8208 


16416 
8208 


9700 


14960 
14550 


4100 
4850- 


•nearly. 


16423 
16416 


MANUFACTURING. 


321 


What  number  of  ends  must  there  be  in  a  warp,  to  fill  39^ 
inches  in  a  Bolton  44  reed ;  if  there  be  19  dents,  or  38  ends  to 
a  beer  ? 


44,  count  of  reed. 

38  ends,  or  19  dents  to  a  beer. 


352 
132 


1672 

39.5,  or  39J  inches,  width  of 

  warp  at  the  reed. 

8360 

15048 

5016 


No.  of  beers  set  on  24.25  in.)66044.00(2723  ends  required  for 

4850  the  warp. 


17544 
16975 


5690 
4850 

8400 
7275 


125 


What  number  of  inches  will  2724  ends  fill  in  a  44  reed,  Bolton 
count ;  allowing  19  dents,  or  38  ends  to  a  beer? 

44,  count  of  reed. 

38  ends,  or  19  dents  to  a  beer. 

352 
132 


1672  divisor. 


322 


MANUFACTURING. 


2724  number  of  ends  in  the  warp. 
24.25,  or  24|  inches,  number  of  beers  set  on. 


13620 
5448 

10896 

5448 


1672)66057.00(39.5,  or  39i  inches,  width  filled  at 
5016  the  reed. 


15897 
15048 


8490 
8360 


130 

What  number  of  ends  must  there  be  in  a  warp,  to  fill  51J 
inches,  in  a  6-4ths  110  reed,  Preston  count  ? 

110,  count  of  reed,  6-4ths  Preston. 
40  ends,  or  20  dents  in  a  beer. 


4400 

51.5,  or  51|  inches,  width  of  warp 

  at  the  reed. 

22000 
4400 
22000 


No.  of  beers  set  on58in.)226600.0(3907.  No.  of  ends  required 

174  for  the  warp. 


526 

522 


400 

406 — nearly. 

What  number  of  inches  will  3907  ends  fill,  in  a  6-4ths  110 
reed,  Preston  count  ? 


MANUFACTUKING. 


323 


110  count  of  reed,  6-4ths  Preston. 
40  ends,  or  20  dents  to  a  beer. 


4400  divisor. 

3907,  number  of  ends  in  the  warp. 
Number  of  beers  set  on     58  inches. 


81256 
19535 


4400)226606(51.5,  or  51i  inches,  width  filled 
22000  at  the  reed. 


6606 
4400 


22060 
22000 


60 

iV.  B. —  The  GAths  Preston  count  of  reeds,  is  the  number  of  heers 
set  on  58  inches,  20  dents,  or  40  etids  to  a  beer. 

The  small  difference  which  appears  in  the  last  two  examples 
arises  from  the  decimal  of  an  end. 

What  number  of  ends  must  there  be  in  a  warp,  to  fill  51J 
inches,  in  a  6-4ths  144  reed,  Preston  count  ? 

144,  number  of  beers  set  on  58  inches  at  the  reed. 
40  ends,  or  20  dents  to  a  beer. 


5760 

51.5,  or  51J  inches,  width  of  warp  at  the  reed. 


28800 
5760 
28800 


296640.0 


324 


MANUFACTURING. 


58  inclies.)296640. 0(5114,  number  of  ends  required  for  the  warp. 

290 


66 
58 

84 
58 


260 
232 

28 


What  number  of  inches  will  5114  ends  fill,  in  a  6-4ths  144 
reed,  Preston  count? 

144,  count  of  reed. 


40  ends,  or  20  dents  to  a  beer. 


5760  divisor. 

5114,  number  of  ends  in  the  warp. 
Number  of  beers  set  on     58  inches. 


40912 
25570 


5760)296612(51.5,  or  51i  inches,  filled  at  the 
28800  reed. 


8612 
5760 


28520 

28800— nearly. 

N.  B. — The  divisor  is  ascertained  hy  multiplying  the  number  of 
beers  set  on  any  given  number  of  inches  {according  to  the 
adopted  rule),  by  the  number  of  ends  in  a  beer  at  the  reed; 
and  the  dividend  by  multiplying  the  number  of  ends  in  the 
warp,  by  the  number  of  inches  any  given  number  of  beers  is 
set  on  at  the  reed. 


MANUFACTURING. 


325 


What  number  of  ends  must  there  be  in  a  warp  to  fill  40J 
inches,  in  a  9-8ths  125  reed,  Preston  count? 

125,  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


5000 

40.5,  or  40|^  inches,  width  of  warp  at 
  the  reed. 


25000 
200000 


No.  of  beers  set  1   44)202500.0(4602,  number  of  ends  required 
on  mcnes.      l  n  ,t 

'      •'  7o  lor  the  warp. 


265 
264 


100 


12 


What  number  of  inches  will  a  warp  containing  4602  ends  fill, 
in  a  9-8ths  125  reed,  Preston  count? 

125  count  of  reed. 

40  ends,  or  20  dents  in  a  beer. 


5000  divisor. 

4602  number  of  ends  in  the  warp. 
Number  of  beers  set  on     44  inches. 


18408 
18408 


5.000)202.488 


40.4976,  or  nearly  40J  inches,  width  the 
warp  fills  at  reed. 


iV.  B. — The  9-8ths  Preston  count  of  reeds  is  calculated  according 
to  the  number  of  beers  set  on  44  inches,  20  dents  to  a  beer. 


326 


MANUFACTURING. 


When  calculating  the  width  at  the  reed  any  -warp  will  fill  ac- 
cording to  the  number  of  ends,  the  count  of  the  reed  must  be 
multiplied  by  the  number  of  ends  filling  1  beer  at  the  reed,  for 
a  divisor,  whether  2,  3,  4,  or  more  ends  be  in  a  dent,  which  will 
be  according  to  the  kind  of  goods  made. 

What  number  of  ends  must  there  be  in  a  warp,  to  fill  39| 
inches,  in  a  9-8ths  105  reed,  Preston  count? 

105,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


4200 

39.5,  or  39J  inches,  width  of  warp 

  at  the  reed. 

21000 
37800 
12600 


No.  of  beers  set  on  44  in. )165900. 0(3770  number  of  ends  required 
132  for  the  warp. 


339 
308 


310 
308 

20 

What  number  of  inches  will  a  warp  containing  3770  ends  fill, 
in  a  9-8ths  105  reed,  Preston  count? 

105,  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


4200  divisor. 

3770  number  of  ends  in  the  warp. 
No.  of  beers  set  on    44  inches. 


15080 
15080 


165880 


MANUFACTURING. 


327 


4200)165880(89.49,  or  39J  inches,  width  filled  at 


39880 
37800 


20800 
16800 


40000 
37800 


2200 


iV.  B. — Some  manufacturers  in  Preston  count  their  9-8t7is, 
AAths,  and  T-Sths  reeds,  in  the  same  proportioyi  to  a  6-4i7iS, 
set  on  58  inches. 

What  number  of  ends  must  there  be  in  a  warp,  to  fill  37 
inches  in  a  4-4th,  or  yard  wide  115  reed,  Preston  count? 


115,  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


4600 

37  inches,  width  of  warp  at  the  reed. 


32200 
13800 


170200 


No.  of  beers  set  on  39  in.)170200(4364  number  of  ends  required 


250 
234 


160 

156 


4 


12600 


the  reed. 


156 


for  the  warp. 


142 
117 


How  many  inches  will  a  warp  containing  4364  ends  fill,  in  a 
4-4ths,  or  yard  wide  115  reed,  Preston  count? 


328 


MANUFACTURING. 


115,  count  of  reed. 

40  ends,  or  20  dents  to  a  beer. 


4600  divisor. 

4364  number  of  ends  in  the  warp. 
Number  of  beers  set  on     39  inches. 


39276 
13092 


4600)170196(36.999,  or  87  inches,  width  the  warp 
13800  fills  at  reed. 


32196 
27600 


45960 
41400 


45600 
41400 


42000 
41400 


600 

N".  B. — The  AAths,  or  yard  tvide  Preston  count  of  reed,  is  calcu- 
lated according  to  the  number  of  beers  set  on  39  inches,  20 
dents  to  a  beer. 

What  number  of  ends  must  there  be  in  a  warp,  to  fill  34J 
inches,  in  a  4-4ths,  or  yard  wide  reed,  Preston  count  ? 

96,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


3840 

34.5,  or  34J  inches  width  of  warp  at 

■   the  reed. 

19200 
15360 
11520 


132480.0 


MANUFACTURING. 


329 


No.  of  beers  set  on  39  in.)132480. 0(3397,  number  of  ends  required 
117  for  the  warp. 


154 
117 


378 
351 

270 

273 — nearly. 

How  many  inches  will  a  warp  containing  3397  ends  fill,  in  a 
4-4ths  or  yard  wide  96  reed,  Preston  count  ? 

96,  count  of  the  reed. 
40  ends,  or  20  dents  to  a  beer. 


3840  divisor. 

3397  number  of  ends  in  the  warp. 
No.  of  beers  set  on  39  inches. 


30573 
10191 


3840)132483(34.5,  or  34i  inches,  warp  fills 
11520  at  the  reed. 


17283 
15360 


19230 
19200 


30 

N.B. — The  9-8^As  set  on  43 J  inches;  the  4-4i7«s,  or  yard  wide, 
set  on  38f  inches,  and  the  7-8ths  set  on  33 1  inches,  will  be  in 
proportion  to  the  6Aths  reed  being  set  on  58  inches. 
22 


330 


MANUFACTURING, 


What  number  of  ends  must  there  be  in  a  warp,  to  fill  32| 
inches,  in  a  T-Sths  66  reed,  Preston  count? 

66,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


2640 

32.5,  or  32|  inches,  width  of  warp  at 
  the  reed. 

13200 

6280 
7920 


No.  of  brs.  seton  34  in. )85800. 0(2523  number  of  ends  required  for 
68  the  warp. 


178 
170 


80 
68 


120 
102 


18 

How  many  inches  will  a  warp  containing  2523  ends  fill,  in  a 
7-8ths  66  reed,  Preston  count  ? 

66,  count  of  reed. 
40  ends,  or  20  dents  to  a  beer. 


2640  divisor. 

2523  number  of  ends  in  the  warp. 
Number  of  beers  set  on    34  inches. 


10092 
7569 


85782 


I 


MANUFACTURING.  331 

2640)85782(32.49,  or  32i  inches,  warp  fills  at  the 
7920  reed. 


6582 
5280 


13020 
10560 


24600 
23760 


840 

y.B. — 77ie  7-8tJis  Preston  count  of  reeds  is  calculated  hy  the 
number  of  beers  set  on  34  inches,  20  dents  to  a  beer. 

What  number  of  ends  must  there  be  in  a  nankeen  warp,  to 
fill  31J  inches,  in  a  60  reed  ? 

60,  count  of  reed. 

38  ends,  or  19  dents  to  a  beer. 


480 
180 


2280 

31.5,  or  31A^  inches,  width  of  warp 
■   at  the  reed. 

11400 

2280 
6840 


No.  of  brs.  set  on,  2.0in.)7182.0.0 


3591  No.  of  ends  required  for  the  warp. 

What  number  of  ends  must  there  be  in  a  nankeen  warp,  to  fill 
21  inches,  in  a  48  reed  ? 


332  MANUFACTURING. 

48,  count  of  reed. 

88  ends,  or  19  dents  to  a  beer. 


384 
144 


1824 

21  inches,  width  of  warp  at  the  reed 


1824 
3648 


No.  of  beers  set  on  2.0  in.)3830.4 

1915  No.  of  ends  required  for  the  warp. 

What  number  of  inches  will  a  nankeen  warp  containing  1915 
ends  fill,  in  a  48  reed? 

48,  count  of  reed. 
38  ends  in  a  beer. 


384 
144 


1824  divisor. 

1915,  number  of  ends  in  the  warp. 
20  inches,  number  of  beers  set  on. 


1824)38300(21  inches,  width  warp  fills  at  the  reed, 
3648 


1820 

1824— nearly. 

^. —  The  nanJceen  count  of  reeds  is  calculated  hy  the  number 
of  leers  set  on  20  inches,  19  dents  to  a  beer. 

How  many  ends  must  there  be  in  a  warp,  to  fill  51|  inches, 
in  a  1850  reed,  Scotch  count? 


t 


MANUFACTURING. 


333 


1850,  count  of  reed. 

51.5,  or  51J  inches,  width  of  warp 

  at  the  reed. 

9250 
1850 
9250 


95275.0 

2  ends  in  a  dent,  or  split. 


No  of  dents  set  on  37  in.)190550(5150  number  of  ends  required 
185  for  the  warp. 


55 
37 


185 
185 


0 

Now  many  inches  will  a  warp  containing  5150  ends  fill,  in  a 
1850  reed,  Scotch  count  ? 

1850,  count  of  reed. 

2,  number  of  ends  in  a  dent,  or  split. 


3700  divisor. 

5150,  number  of  ends  in  the  warp. 
Number  of  dents  set  on    37  inches. 


36050 
15450 


3700)190550(51.5,  or  51J  inches,  warp  fills  at 
18500  the  reed. 


5550 
3700 


18500 
18500 


334 


MANUFACTURING. 


iV.  B. — In  Carlisle,  Scotland,  Ireland,  and  the  United  States  of 
America,  they  calculate  their  reeds  hy  the  number  of  dents  set 
on  37  inches. 

In  Carlisle  and  Scotland  a  dent  is  generally  termed  a  split. 

How  many  ends  must  there  be  in  a  warp,  to  fill  49  J  inches,  in 
a  2150  reed,  Scotch  count  ? 

2150,  count  of  reed. 

2,  number  of  ends  in  a  dent, 

  or  split. 

4300 

49.5,  or  49J  inches,  width  of  warp 

  at  the  reed. 

21500 
38700 
17200 


No.  of  dents  set  on  37  in.)212850.0(5752,  number  of  ends  re- 

185  quired  for  the  warp. 


278 
259 


195 
185 


100 
74 


26 

How  many  inches  will  a  warp  containing  5752  ends  fill,  in  a 
2150  reed,  Scotch  count? 

2150,  count  of  reed. 

2,  number  of  ends  in  a  dent,  or 

  split. 

4300  divisor. 

5752,  number  of  ends  in  the  warp. 
Number  of  dents  set  on    37  inches. 


40264 
17256 


212824 


MANUFACTURING. 


335 


4300)212824(49.49,  or  49|-  inches,  nearly, 
17200  warp  fiUa  at  the  reed. 


40824 
38T00 


21240 
17200 


40400 
38700 


1700 

must  there  be  in  a  silk  warp,  to  fill  19 

3700,  count  of  reed. 

19  inches,  width  of  warp  required 
  at  the  reed. 

33300 
3700 


No.  of  ends  in  36  in.)70300(1952  number  of  ends  required 
36  for  the  warp. 


343 
324 


190 
180 


100 
72 


28 

How  many  inches  will  a  silk  warp  containing  1952  ends  fill, 
in  a  3700  reed  ? 

1952  number  of  ends  in  the  warp. 
Number  of  ends  in     36  inches. 


11712 

6856 


What  number  of  ends 
inches,  in  a  3700  reed  ? 


70272 


336 


LINEN  YARNS. 


Count  of  reed  3700)70272(18.99,  or  19  inches,  nearly,  width 
3700  the  warp  fills  at  the  reed. 


33272 
29600 


36720 
33300 


34200 
33300 


900 

iV.  B. — The  silk  manufacturers  generally  calculate  their  reeds  hy 
twice  the  7iumher  of  dents,  or  the  number  of  ends  in  36  inches 
at  the  reed. 


LINEN  YARN  TABLES. 

Showing  the  weight  of  1  lea,  or  cut,  English  hank  and  bundle, 
Irish  and  Scotch  hank,  spangle,  or  spindle,  and  bundle,  from  1 
to  300  leas  or  cuts  in  the  pound  progressively. 


The  following  are  the  different  sizes  of  reels  in  use,  with  the 
different  systems  of  making  up  yarns. 

YORKSHIRE  REEL. 

3  yards,  or  108  inches  in  circumference. 
100  threads,  1  lea,  300  yards. 
10  leas,  1  hank,  3.000  yards. 
20  hanks,  1  bundle,  60.000  yards. 
Sells  per  bundle. 

DORSET  REEL. 

2\  yards,  or  81  inches  in  circumference. 
40  threads,  1  knot,  90  yards. 
20  knots,  1  ran,  1.800  yards. 
12  rans,  1  dozen,  21.600  yards. 
Sells  per  dozen. 

N.  B. — This  reel  is  not  much  in  use,  the  Irish  reel  being  gene- 
rally adopted. 


LINEN  YARNS.  [  /  387  X 

IRISH  AND  SCOTCH  REELS.        >  <.  .  '  i/-;-^.  \ 

yards,  or  90  inches  in  circumference. V,>  ^  ^  -  / 
120  threads,  1  cut,  300  yards.  -^-5 j-,.-'^"' 
12  cuts,  1  hank,  3.600  yards. 
4  hanks,  1  spangle,  14.400  yards. 
12J  spangles,  or  60  hanks,  1  bundle,  180.000  yds. 
Sells  per  spangle  in  bundles. 


POINTS  IN  WHICH  THE  THREE  REELS  AGREE.  . 

40  knots,  or  2  rans,  make  1  hank  Irish  and  Scotch,  3.600  yards. 
8  hanks  Dorset,  or  4  hanks  Irish  and  Scotch,  make  1  spangle  or 

spindle,  14.400  yards. 
1^  spangles  or  spindles,  make  1  dozen  Dorset,  21.600  yards. 
12J  spangles  or  spindles,  or  50  hanks  Irish  and  Scotch,  or  8 

English  bundles  of  60.000  yards  each,  make  1  Irish  bundle, 

180.000  yards. 


EXPLANATION  TO  THE  LINEN  YARN  TABLES. 

The  first  column  is  the  numbers  of  yarn,  opposite  to  which  is 
the  weight  according  to  the  length  weighed. 

JV.  B. — The  pounds  and  ounces  are  avoirdupois  weight,  and  the 
pennyweights  and  grains  are  troy  loeight. 

oz.  dwts.  grains,  grains. 

14    11       16   or  7000  troy  are  equal  to  1  lb.  avoirdupois. 
18         5J  or  437J  troy  are  equal  to  1  oz.  avoirdupois. 

The  following  are  the  dividends  according  to  the  length  weighed. 


Yards.  Dividends. 

1  lea,  or  cut                   300  7.000 

1  English  hank             3.000  70.000 

1  Irish  and  Scotch  hank  3.600  84.000 

1  spangle  or  spindle     14.400  336.000 

1  English  bundle         60.000  1.400.000 

1  Irish  bundle           180.000  4.200.000 

1  knot,  Dorset                 90  2.100 

1  ran,       do.               1.800  42.000 

1  dozen,    do.             21.600  504.000 


JV.  B. — By  dividing  any  of  the  above  dividends,  according  to  the 
length  weighed,  by  the  number  of  grains  in  the  weight,  it  will 
give  the  numbers  of  yarns  ;  or  divide  by  the  numbers  of  yarns, 
and  it  ivill  give  the  number  of  grains  weight,  according  to  the 
length  weighed. 


338  LINEN  YARNS. 

LINEN  YARN  TABLE. 


From  Number  1  to  110  leas  or  cuts  in  the  pound. 


Weight  per  lea  or  cut  of 

Weight  per  English  hank 

Weight  p 

Br  English  bun- 

300  yards. 

of  3000  yards. 

die  of  60,000  yards. 

Nos. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

1 

16 

0 

0. 

10 

0 

0 

0. 

200 

0 

0 

0. 

2 

8 

0 

0. 

5 

0 

0 

0. 

100 

0 

0 

0. 

3 

5 

6 

1.83 

3 

5 

6 

1.83 

66 

10 

12 

3.66 

4 

4 

0 

0. 

2 

8 

0 

0. 

50 

0 

0 

0. 

5 

3 

3 

15.5 

2 

0 

0 

0. 

40 

0 

0 

0. 

6 

2 

12 

3.66 

1 

10 

12 

3.66 

33 

5 

6 

1.83 

7 

2 

5 

5. 

1 

6 

15 

15. 

28 

9 

2 

14.5 

8 

2 

0 

0. 

1 

4 

0 

0. 

25 

0 

0 

0. 

9 

1 

14 

4.27 

1 

1 

14 

4.27 

22 

3 

10 

3.05 

10 

1 

10 

22.5 

1 

0 

0 

0. 

20 

0 

0 

0. 

11 

1 

8 

6.83 

14 

9 

22.63 

18 

2 

16 

13.72 

12 

1 

6 

1.83 

13 

6 

1.83 

16 

10 

12 

3.66 

13 

1 

4 

4.96 

12 

5 

14.61 

15 

6 

2 

19.3 

14 

1 

2 

14.5 

11 

7 

19.5 

14 

4 

10 

10. 

15 

1 

1 

5,16 

10 

12 

3.6 

13 

5 

6 

1.83 

16 

1 

0 

0. 

10 

0 

0. 

12 

8 

0 

0. 

17 

17 

3.76 

9 

7 

12.14 

11 

12 

4 

6.94 

18 

16 

4.88 

8 

16 

4.88 

11 

1 

14 

4.27 

19 

15 

8.41 

8 

7 

16.21 

10 

8 

7 

16.21 

20 

14 

14. 

8 

0 

0. 

10 

0 

0 

0. 

25 

11 

16. 

6 

7 

7. 

8 

0 

0 

0. 

30 

9 

17.33 

5 

6 

1.83 

6 

10 

12 

3.66 

35 

8 

8. 

4 

10 

10. 

5 

11 

7 

19.5 

40 

7 

7. 

4 

0 

0. 

5 

0 

0 

0. 

45 

6 

11.55 

3 

10 

3.05 

4 

7 

2 

0.61 

50 

5 

20. 

3 

3 

15.5 

4 

0 

0 

0. 

55 

5 

7.25 

2 

16 

13.72 

3 

10 

3 

7.54 

60 

4 

20.66 

2 

12 

3.66 

3 

5 

6 

1.83 

65 

4 

11.69 

2 

8 

9.92 

3 

1 

4 

4.96 

70 

4 

4. 

2 

5 

5. 

2 

13 

13 

0.5 

75 

3 

21.33 

2 

2 

10.33 

2 

10 

12 

3.66 

80 

3 

15.5 

2 

0 

0. 

2 

8 

0 

0. 

85 

3 

10.35 

1 

16 

2.02 

2 

5 

11 

19.08 

90 

3 

5.77 

1 

14 

4.27 

2 

3 

10 

3.05 

95 

3 

1.68 

1 

12 

11.3 

2 

1 

12 

11.34 

100 

2 

22. 

1 

10 

22.5 

2 

0 

0 

0. 

105 

2 

18.66 

1 

9 

13.1 

1 

14 

8 

6.33 

110 

2 

15.63 

1 

8 

6.8 

1 

13 

1 

15.77 

LINEN  YARNS,  339 

Required,  the  weight  of  1  lea  of  number  IS's  yarn? 
Dividend. 

Numbers  of  yarn,  18)7000(388.8  grains,  or  16  dwts.,  4|  grains, 
54  weight  required. 


160 
144 

  160 

160  144 
144   

  16 

Required,  the  weight  of  1  English  hank  of  number  18's  yarn  ? 
Dividend. 

Numbers  of  yarn,  18)70000(3888.88  grains,  or  8  oz.,  16  dwts., 
54  4|  grains,  weight  required. 


160 
144 


  160 

160  144 
144   


160 


160  144 

144   

  16 


How  many  ounces,  pennyweights,  and  grains,  are  there  in 
3888.88  grains  ? 

Grains.  Grains. 
1  oz.  is  equal  to  437.5)3888.88(8  ounces. 

35000 


1  pennyweight  is  24  grs.)388. 88(16  dwts. 

24 


148 
144 


grains. 


8  oz.,  16  dwts.,  4.88  grains,  weight  required. 


340  LINEN  YARNS. 

LINEN  YARN  TABLE* 


From  Number  1  to  110  leas  or  cuts  in  1  pound. 


Weight  per  Irish  and 
Scotch  hank  of  3600  yards. 

Weight  per  spangle  or 
spindle  of  14,400  yards. 

Weight  per  Irish 
bundle  of  lbO,000  yards. 

Nos. 

lbs. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

1 

12 

0 

0 

0. 

48 

0 

0 

0. 

600 

0 

0 

0. 

2 

6 

0 

0 

0. 

24 

0 

0 

0. 

300 

0 

0 

0. 

3 

4 

0 

0 

0. 

16 

0 

0 

0. 

200 

0 

0 

0. 

4 

3 

0 

0 

0. 

12 

0 

0 

0. 

150 

0 

0 

0. 

5 

2 

6 

7 

7. 

9 

9 

10 

22.5 

120 

0 

0 

0. 

6 

2 

0 

0 

0. 

8 

8 

0 

0. 

100 

0 

0 

0. 

7 

1 

11 

7 

19.5 

6 

13 

13 

0.5 

85 

11 

7 

19.5 

8 

1 

8 

0 

0. 

6 

0 

0 

0. 

75 

0 

0 

0. 

9 

1 

5 

6 

1.83 

5 

5 

6 

1.83 

66 

10 

12 

3.6 

10 

1 

3 

3 

15.5 

4 

12 

14 

14. 

60 

0 

0 

0. 

11 

1 

1 

8 

6.86 

4 

5 

14 

21.95 

54 

8 

13 

6.1 

12 

1 

0 

0 

0. 

4 

0 

0 

0. 

50 

0 

0 

0. 

13 

14 

14 

0.53 

3 

11 

1 

9.65 

46 

2 

8 

9.9 

14 

13 

13 

0.  5 

3 

6 

15 

15. 

42 

13 

13 

0.5 

15 

12 

14 

14. 

3 

3 

3 

15.5 

40 

0 

0 

0. 

16 

12 

0 

0. 

3 

0 

0 

0. 

37 

8 

0 

0. 

17 

11 

5 

8.67 

2 

13 

3 

5.2 

35 

4 

12 

20.8 

18 

10 

12 

3.66 

2 

10 

12 

3.66 

33 

5 

6 

1.8 

19 

10 

1 

22.05 

2 

8 

7 

16.21 

31 

9 

4 

19.1 

20 

9 

10 

22.5 

2 

6 

7 

7. 

30 

0 

0 

0. 

25 

7 

12 

9.5 

1 

14 

13 

3. 

24 

0 

0 

0- 

30 

6 

7 

7. 

; 

9 

10 

22.5 

20 

0 

0 

0. 

35 

5 

8 

20.5 

5 

17 

4.5 

17 

2 

5 

5. 

40 

4 

14 

14. 

3 

3 

15.5 

15 

0 

0 

0. 

45 

4 

4 

20.66 

1 

1 

5.16 

13 

5 

6 

1.8 

50 

15 

7.5 

15 

6 

13.5 

12 

0 

0 

0. 

55 

3 

8 

22.77 

13 

17 

13.59 

10 

14 

9 

22.6 

60 

3 

3 

15.5 

12 

14 

14. 

10 

0 

0 

0. 

65 

2 

17 

9.3 

11 

14 

20.73 

9 

3 

12 

14.8 

70 

2 

13 

13. 

10 

17 

17. 

8 

9 

2 

14.5 

75 

2 

10 

5. 

10 

4 

9. 

8 

0 

0 

0. 

80 

2 

7 

7. 

9 

10 

22.5 

7 

8 

0 

0. 

85 

2 

4 

17.23 

9 

0 

15.44 

7 

0 

17 

3.7 

90 

2 

2 

10.33 

8 

9 

17.33 

6 

10 

12 

3.6 

95 

2 

0 

9.21 

8 

1 

12.84 

6 

5 

0 

23.0 

100 

1 

16 

18.5 

7 

12 

9.5 

6 

0 

0 

0. 

105 

1 

15 

2.5 

7 

5 

17.5 

5 

11 

7 

19.5 

110 

1 

13 

14.13 

6 

17 

21.54 

7 

4 

23.3 

LINEN  YABNS.  341 

Required,  the  weight  of  1  spangle  of  number  19's  yarn  ? 
Dividend. 

Numbers  of  yarn,  19)83600(17684.2  grains,  weight  required. 


19 

146 

133 

130 

114 

160 

152 

40 

80 

38 

76 

2 

How  many  pounds,  ounces,  and  pennyweights  are  there  in 
17684.2  grains  ? 

Grains.  Grains. 
1  lb.  is  equal  to  7000)17684.2(2  lbs.,  8  oz.,  7  dwts.,16|  grains. 

14000 


1  oz.  is  equal  to  437.5  grs.)3684.2(8  oz. 

35000  . 


1  dwt.  is  equal  to  24  grs.)184.2(7  dwts. 


16^  grains. 

Required,  the  weight  of  1  English  bundle  of  number  34's  yarn? 
Dividend. 

Numbers  of  yarn,  34)1400000(41176  grains,  or  5  lbs.,  14  oz.,  2 
136  dwts.,  3  J-  grains. 

  260 

40  238 

34   

  220 

60  204 

34   

  16 


342 


LINEN  YARNS. 


LINEN  YARN  TABLE. 


From  Number  115  to  800  leas  in  1  pound. 


Weight  per  lea,  or 
cut  of  300  yards. 

1  Weight  per  English 

Weight  per  English  bundle 

hank  of  3000  yards. 

of  60,000  yards. 

Nos. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

115 

2 

12.86 

1 

7 

3.1 

1 

11 

15 

1.41 

120 

2 

10.33 

1 

6 

1.8 

1 

10 

12 

3.66 

125 

2 

8. 

1 

5 

2.5 

1 

9 

10 

22.5 

130 

2 

5.84 

1 

4 

4.96 

1 

8 

11 

5.23 

135 

2 

3.85 

1 

3 

9.03 

1 

7 

12 

19.87 

140 

2 

2. 

1 

2 

14.5 

1 

6 

15 

14. 

145 

2 

0.27 

1 

1 

21.25 

1 

6 

1 

6.17 

150 

1 

22.66 

1 

1 

5.18 

1 

5 

6 

1.83 

155 

1 

21.16 

1 

0 

14.11 

1 

4 

11 

18.25 

160 

1 

19.75 

1 

0 

0. 

1 

4 

0 

0. 

165 

1 

18.42 

17 

16.24 

1 

3 

7 

4.34 

170 

1 

17.17 

17 

3.74 

1 

2 

15 

0.29 

175 

1 

16. 

16 

16. 

1 

2 

5 

5. 

180 

1 

14.88 

16 

4.88 

1 

1 

14 

4.27 

185 

1 

13.83 

15 

18.37 

1 

1 

5 

10.06 

190 

1 

12.84 

15 

8.42 

1 

0 

15 

8.42 

195 

1 

11.89 

14 

22.97 

1 

0 

7 

11.48 

200 

1 

11. 

14 

14. 

1 

0 

0 

0. 

205 

1 

10.14 

14 

5.46 

15 

11 

2.76 

210 

1 

9.33 

13 

21.33 

15 

4 

8.16 

215 

1 

8.55 

13 

.13.58 

14 

16 

2.62 

220 

1 

7.81 

13 

6.18 

14 

9 

22.63 

225 

1 

7.11 

12 

23.11 

14 

4 

1.22 

230 

1 

6.43 

12 

16.34 

13 

16 

15.45 

zoo 

i 

0.  /  0 

li 

O.VO 

240 

1 

5.16 

12 

3.66 

13 

6 

1.83 

245 

1 

4.571 

11 

21.71 

13 

1 

2.785 

250 

1 

4. 

11 

16. 

12 

14 

14. 

255 

1 

3.45 

11 

10.5 

12 

10 

0.196 

260 

1 

2.923 

11 

5.23 

12 

5 

14.615 

265 

1 

2.414 

11 

0.14 

12 

9.018 

270 

1 

1.925 

10 

19.25 

11 

il 

12.685 

275 

1 

1.454 

10 

14.54 

11 

11 

14. 

280 

1 

1. 

10 

10. 

11 

7 

19. 

285 

1 

0.561 

10 

5.67 

11 

4 

3. 

290 

1 

0.137 

10 

1.37 

11 

•  0 

15. 

295 

23.728 

9 

21.28 

10 

15 

10. 

800 

23.333 

9 

17.33 

10 

12 

8. 

I 


LINEN  YARNS.  343 

Required,  the  weight  of  1  Irish  bundle  of  66's  yarn. 

Numbers  of  yarn,  66)4200000(63636.36  grains. 
396 


240 
198 


420 

396 

240 
198 


420 

396 


240 
198 


420 
396  ■ 


24 

Grains.  Grains. 

1  lb.  is  equal  to  7000)63686.36(9  lbs.,  1  oz.,  8  dwts.,  6.86  grs. 

63000  weight  required. 


1  oz.  is  equal  to  437.5  grs.)636.36(l  oz. 

4375 


8  dwt.  is  equal  to  24  grns.)198.86(8  dwts. 

192 


6.86  grains. 


344  LINEN  YARNS. 

Or, 

lbs. 

Numbers  of  yarn,  66)600(9  lbs.,  1  oz.,  8  dwts.,  6.86  grains, 

594  weight  required. 

6 

16  oz.,  1  lb. 


Numbers  of  yarn,  66)96(1  oz. 

66 


30 

487.5  grains,  1  oz. 


Nos.  of  yarn,  66)13125.0(198.86  grains  or  8  dwts.,  6.86  gra. 
66 

652 
594 

585 
528 

570 
528 

42 


t 


LINEN  TARNS. 


345 


LINEN  YARN  TABLE. 


From  Number  115  to  300  leas,  or  cuts  in  1  pound. 


Weight  per  Irish  and 

Weight  per  spangle  or 

Weight  per  Irish  bundle  of 

Scotch  hank  of  3600  yards. 

spindle  of  H,400  yds 

180,000  yards. 

Nos. 

oz. 

d  w  ts . 

grains. 

uz. 

gfiiinSi 

lbs. 

OZ. 

d  wts 

grains. 

115 

12 

4.93 

6 

12 

8.74 

o 

3 

8 

17.23 

120 

10 

22.5 

G 

7 

7. 

F, 

0 

0 

0. 

125 

9 

18.5 

6 

2 

15. 

A 

4: 

12 

14 

14. 

130 

8 

16.65 

5 

16 

13.11 

A 
'i 

9 

15 

10.19 

135 

7 

16.72 

5 

12 

13.38 

4. 

7 

2 

0.61 

140 

6 

18.5 

5 

8 

20.5 

A 
rt 

4 

10 

10. 

146 

5 

21.81 

5 

5 

9.74 

A 

2 

3 

18.51 

150 

5 

2.5 

5 

2 

4.5 

A 

0 

0 

0. 

155 

4 

8.43 

4 

17 

9.74 

Q 
O 

13 

17 

1.37 

160 

3 

15.5 

4 

14 

14. 

O 

12 

0 

0. 

165 

2 

23.59 

4 

11 

22.36 

Q 
O 

10 

3 

7.54 

170 

2 

8.61 

4 

9 

10.47 

Q 
O 

8 

8 

13.87 

175 

1 

18.5 

4 

7 

2. 

6 

15 

15. 

180 

1 

5.16 

4 

4 

20. ()6 

Q 
O 

5 

6 

1.83 

185 

0 

16.55 

4 

2 

18.21 

9 

o 

3 

16 

6.2 

190 

0 

4.6 

4 

0 

18.42 

Q 

o 

2 

9 

14.26 

195 

17 

22.76 

3 

17 

2.57 

o 

1 

4 

4.96 

200 

17 

12. 

3 

15 

7  5 

q 

0 

0 

0. 

205 

17 

1.756 

3 

13 

14.52 

2 

14 

15 

2.8 

210 

16 

16. 

3 

11 

23.5 

0 

13 

13 

0.5 

215 

16 

6.69 

o 
ij 

10 

10.29 

9 

12 

11 

20.88 

220 

15 

21.81 

3 

8 

2">  77 

o 
z 

11 

11 

14.41 

225 

15 

13.33 

3 

7 

12.84 

10 

12 

3.66 

230 

15 

5.21 

3 

6 

4^37 

2 

9 

13 

1L36 

235 

14 

21.44 

3 

4 

21.28 

2 

8 

15 

12.34 

240 

14 

14. 

3 

3 

15.5 

2 

8 

0 

0. 

245 

14 

6.857 

3 

2 

10.928 

2 

7 

3 

8.357 

250 

14 

0. 

3 

1 

7.5 

2 

6 

7 

7. 

255 

13 

17.411 

3 

0 

5.147 

2 

5 

11 

19.088 

260 

13 

11  076 

2 

17 

9.307 

2 

4 

16 

19.846 

265 

13 

4.981 

2 

16 

8.924 

2 

4 

4 

3.054 

270 

12 

23.111 

2 

15 

9.444 

2 

3 

10 

3.055 

275 

12 

17.45 

2 

14 

10.81 

2 

16 

17.72 

280 

12 

12. 

2 

13 

13. 

I 

2 

5 

5. 

285 

12 

6.73 

0 

12 

15.94 

1 

12 

11.34 

290 

12 

1.65 

2 

11 

19.62 

2 

1 

1 

21.25 

295 

11 

20.74 

2 

10 

23.98 

2 

0 

9 

21.28 

300 

11 

16. 

2 

10 

5. 

2 

0 

0 

"  1 

23 


346  LINEN  YARNS. 

Required,  the  weight  of  an  Irish  or  Scotch  hank  of  number 
68's  yarn  :■ — 

Dividend. 

Numbers  of  yarn,  68)84000(1235.29  grains. 
68 


160 
136 


240 
204 


360 
340 


200 
136 


640 
612 


28 

Grains.  Grains. 

1  oz.  is  equal  to  437.5)1235.29(2  oz.,  15  dwts.,  0.29  grains,  wt. 

8750  required. 

Idwt.  isequalto24grns.)360.29(15  dwts. 

24 


120 
120 


0.29  grain. 

How  many  yards  are  there  in  1  lb.  and  in  1  oz.  of  number  68*3 
yarn  ? 

300  yards  is  1  lea,  or  cut. 
Numbers  of  yarn,  68 


20400  number  of  yards  in  1  lb. 


LINEN  TARNS.  347 

1  lb.  is  equal  to  16  oz.)20400(1275  yards  in  1  oz. 
16 


44 
32 

120 
112 


80 
80 

Required,  the  weight  of  1  spangle  of  number  85's  yarn: — 
Dividend. 

Numbers  of  yarn,  85)336000(3952.94  grains. 
255 


810 

765 


450 
425 


250 
170 


800 
765 


355 
340 


15 

Grains.  Grains. 

1  oz.  is  equal  to  437.5)3952.94(9  oz.,  0  dwts.,  15.44  grs.,  weight 
39375  required. 


15.44 

If  1  spangle  of  linen  yarn  weighs  9  oz.,  15 J  grains;  what 
nuEQbers  will  it  be  ? 


348  LINEN  YARNS. 

9  OZ,,  15.5  grains. 
437.5  grains  are  equal  to  1  oz. 


3953.0  grains. 

Grains.  Dividend. 
9  oz.,  15J  grns.  are  equal  to  3953)336000(85  leas,  or  cuts  in  1  lb. 

31624  -which  is  the  nos.  of  yarn. 


19760 

19765 — nearly. 

How  many  yards  of  number  85's  yarn  are  there  in  1  lb.  and 
in  1  oz.  ? 

300  yards,  1  lea,  or  cut. 
85,  numbers  of  yarn. 


16  oz.,  1  lb. 


4)25500  yards  in  1  lb. 


4)6375 


1593.75,  or  1593f  yards  in  1  oz. 
Required,  the  ■weight  of  an  Irish,  or  Scotch  hank  of  number 
95's  yarn: — 

Dividend. 

Numbers  of  yarn,  95)84000(884.21  grains,  weight  required. 
760 

800 
760 

400 
380 

200 
190 

100 

95 


5 


1 


LINEN  YARNS.  349 

Grains.  Grains. 

1  oz.  is  equal  to  437.5)884.21(2  oz.,  0  dwts.,  9.91  grains,  weight 
8750  required. 

9.21  grains. 

If  1  Irish  or  Scotch  hank  of  linen  yarn  weighs  2  oz.,  0  dwts., 
9 J  grains,  what  numbers  will  it  be? 

437.5  grains  are  equal  to  1  oz. 
2 


875.0  grains  are  equal  to  2  oz. 
Add       9.25  grains. 


884.25  grs.  is  equal  to  2  oz.,  0  dwts.,  9J  grs. 
Grains.  Dividend. 

884.25)84000.00(9499,  or  nearly  95  numbers  of  yarn. 
795825 


441750 
353700 


880500 
795825 


846750 
795825 


50925 


350  LINEN  YARNS. 

Required,  the  weight  of  1  Irish  hundle  of  number  107 's  yarn  : — 
Dividend. 

Numbers  of  yarn,  107)4200000(39252.83  grains,  weight  required. 
321 


990 
963 


270 
214 


660 
635 


250 
214 


360 
321 


390 
321 


69 

Grains.  Grains. 
1  lb.  is  equal  to  7000)39252.33(5  lbs.,  9  oz.,  13  dwts.,  283 
35000  grains,  weight  required. 

1  oz.  is  equal  to  437.5  grns.)4252.33(9  oz. 

39375 


1  dwt.  is  equal  to  24  grains)314.83(13  dwts. 

24 


74 
72 


2.83  grains. 

If  1  Irish  bundle  of  linen  yarn  weighs  5  lbs.,  9  oz.,  13  dwts., 
2.83  grains,  or  39252.33  grains,  what  number  will  it  be? 


39252.33)4200000.00(107,  numbers  of  yarn. 
3926233 


Grains. 


LINEN  YARNS. 


27476700 
27476631 


69 


Required,  the  weight  of  1  English  bundle  of  number  138's  yarn: — 


Numbers  of  yarn,  138)1400000(10144.927  grs.,  weight  required. 
138 


200 
138 


620 
552 


680 
552 


1280 
1242 


380 
276 


1040 
966 


■74 


1  lb.  is  equal  to  7000)10144.927(1  lb.,  7_oz.,  3  dwts.,  10.427 
7000  grains,  weight  required. 


1  oz.  is  equal  to  437.5  grs.)3144.927(7  oz. 

30625 


1  dwt.  is  equal  to  24  grains)82.427(3  dwts. 

72 


Dividend. 


Grains.  Grains. 


10.427  grains. 


352  LINEN  TARNS. 

If  1  English  bundle  of  linen  yarn  weighs  1  lb.,  7  oz.,  3  dwts., 
10^  grains,  what  numbers  will  it  be  ? 

Grains.  Dividend. 
1  lb.,  7  oz.,  8  dwts.,  lOi  grs.,  =10145)1400000(138,  numbers  of 

10145  yarn  nearly. 

38550 
30485 


81150 

81160— nearly. 

Kequired,  the  weight  of  1  English  hank  of  number  138's  yarn : — 
Dividend. 

Numbers  of  yarn,  138)70000(507.246  grains,  weight  required. 
690 


1000 
966 


340 
276 


640 
552 


880 
828 


52 

Grains.  Grains. 

1  oz,  is  equal  to  437.5)507.246(1  oz.,  2  dwts.,  21f  grns.  nearly, 
4375  weight  required. 

1  dwt.  is  equal  to  24  gr3.)69.746(2  dwts. 

48 


21.746  grains. 


LINEN  YARNS.  353 

Required,  the  weight  of  1  English  bundle  of  number  12S's 
yarn : — 

Dividend. 

Numbers  of  yarn,  128)1400000(10937.5  grains,  weight  required. 
128 


1200 
1152 


480 
384 


9C0 
826 


640 
640 

Grains.  Grains. 
1  lb.  is  equal  to  7000)10937.5(1  lb.,  9  oz.,  weight  required. 
7000 


1  oz.  is  equal  to  437.5  grs.)3937.5(9  oz. 

39375 

Required,  the  weight  of  1  lea,  or  cut  of  154's  yarn: — 
Dividend. 

Numbers  of  yarn,  154)7000(45.45  grains,  or  nearly  1  dwt.,  21i 
616  grains,  weight  required. 

840 
770 


700 
616 


840 
770 


70 


354  LINEN  YARNS. 

Required,  the  weight  of  1  English  hank  of  number  154's 
yarn: — 

Numbers  of  yarn,  154)700000(454.54  grains,  "weight  required. 
616 


840 
770 


700 
616 


840 
770 


700 
616 


84 

How  many  ounces,  pennyweights,  and  grains,  are  there  in 
454.54  grains? 

1  oz.  is  equal  to  437.5  grns.)454. 545454(1. 03896  ounces. 

4375  437.5  grains  =1  oz. 


17045  19480 
13125  27272 

  11688 

39204  15584 

35000   

  17.045000  grs.,  or  1  oz. 

42045  0  dwts.,  17  grns., 

39375  weight  required. 

26704 
20250 


454 


LINEN  YARNS.  355 

Required,  the  weight  of  1  English  bundle  of  number  165's 
yarn  : — ■ 

Dividend. 

'  Numbers  of  yarn,  165)1400000(8484.848  grains,  weight  required. 
1320 


800 
660 


1400 
1320 


800 
660 


1400 
1320 


800 
660 


1400 
1320 


80 

How  many  pounds,  ounces,  pennyweights,  and  grains  are  there 
in  8484.848  grains  ? 

Grains.  Grains. 
1  lb.  =7000)8484.848(1  lb.,  3  oz.,  7  dwts.,  4.348  grains. 
7000 


1  oz.  =437.5  grns.)1484.848(3  oz. 

13125 


1  dwt.=24  grains,)172.348(7  dwts. 
168 


4.348  grains. 

If  1  English  bundle  of  yarn  weighs  1  lb.,  3  oz.,  7  dwts.,  4.348 
grains,  or  1484.848  grains,  what  numbers  will  it  be? 


356  LINEN  YARNS. 

Dividend. 

1  bundle  weighs  8484.848  grns.)1400000.000(165's  nos.  of  yarn. 

8484848 


65151520 
50909088 

42424320 
42424240 


How  many  yards  are  there  in  1  pound  of  184's  yarn  ? 

184,  numbers  of  yarn. 

300  yards  are  1  lea  of  number  1. 


55200,  number  of  yards  in  1  lb. 

Required,  the  weight  of  1  Irish  or  Scotch  hank  of  number 
184's  yarn : — 

Dividend. 

Numbers  of  yarn,  184)84000(456.52  grains,  weight  required. 
736 


1040 
920 


1200 
1104 


960 
920 

400 
368 

Grains.  Grains. 
1  oz.  =437.5)456.52(1  oz.,  0  dwts.,  19.02  grains,  weight  re- 
437.5  quired. 


19.02  grains. 


LINEN  TARNS.  857 

Required,  the  weight  of  1  English  hank  of  number  180'a 
yarn  : — 

Dividend. 

Numbers  of  yarn,  180)70000(388|  grains,  weight  required. 
540 


1600 
1440 


1600 
1440 


160 

1  dwt.  is  equal  to  24  grns.)388|(16  dwts.,  4|  grains,  weight  re- 

-4  quired. 

148 
144 


4  8-9ths. 

Required,  the  weight  of  1  Irish  spangle,  or  Scotch  spindle  of 
number  196's : — 

Dividend. 

Numbers  of  yarn,  196)336000(1714.285  grains,  weight  required. 
196 


1400 
1372 


280 
196 


840 
784 

660 
892 

- —  1120 

1680  980 
1568   


358  LINEN  YARNS. 

Grains.  Grains. 
1  oz.=437.5)1714.285(3  oz.,  16  dwts.,  17.785  grains, 
13125  weight  required. 


1  dwt.=24  grains,)401.785(16  dwts. 
24 


161 
144 


17.785  grains.* 

How  many  yards  are  there'  in  1  oz.  of  number  196's  ? 
196,  numbers,  or  counts  of  yarn. 
300  yards  are  1  lea  of  number  I's. 

1  lb.  =  16  oz.)58800(3675  yards  of  nos.  196's  in  1  oz. 
48 


108 

96 


120 
112 


80 
80 

Required,  the  weight  of  1  lea,  or  cut  of  number  2l5's  weft:  — 
Dividend. 

Numbers  of  yarn,  215)7000(32.558  grains,  or  1  dwt.,  8|  grains, 
645  weight  required. 


550 
430 

1200 
1075 


1250 
1075 


1750 
1720 


30 


LINEN  YARNS.  359 

Required,  the  ■weight  of  1  Irish  or  Scotch  hank  of  number 
235's  yarn: — 

Dividend. 

Numbers  of  yarn,  235)84000(357.446  grains,  vreight  required. 
705 


1  dwt.  =  24  grains,  or 


1350 
1175 

1750 
1645 

1050 
940 

1100 

940 

1600 
1410 

190 

■  4)357.446  grains. 
6)89.3615 


14.89358,  or  14  dwts.,  211  gts,,  nearly. 

How  many  yards  are  there  in  1  pound  of  number  235's  yarn  ? 

235,  numbers  of  yarn. 

300  yards  1  lea,  or  cut  of  number  I's, 


70500  number  of  yards  required. 


860  LINEN  YARNS. 

Required,  the  weight  of  1  Irish  bundle  of  number  130's  yarn: — 
Dividend. 

Numbers  of  yarn,  130)4200000(32307.692  grs.  weight  required. 
390 


300 
260 


400 
390 

1000 
910 


900 
780 

1200 
1170 


300 
260 


40 

Grains.  Grains. 
1  lb.  -7000)32807.692(4  lbs.,  9  oz.,  15  dwts.,  10^  grains 
28000  nearly,  weight  required. 


1  oz.=*437.5  grns.)4307.692f9  oz. 

3937.5 


1  dwt.  =24  grains,)370.192(15  dwts. 
24 


130 
120 


10.192  grains. 

If  1  Irish  bundle  of  yarn  weighs  4  lbs.,  9  oz.,  15  dwts.,  10.192 
grains,  or  32307.692  grains,  what  numbers  will  it  be  ? 


LINEN  YARNS. 


361 


Dividend. 

Weight,  32307.692)4200000.00(130,  numbers  of  yarn. 
32307692 


96923080 
96923076 


40 

Required,  the  weight  of  1  English  hank  of  number  245's 
yarn : — 

Dividend. 

Numbers  of  yarn,  245)70000(285.714  grains,  -weight  required. 
490 


2100 
1960 


1400 
1225 


1750 
1715 


350 
245 

1050 

980 


70 

Grains.  Grains. 
1  dwt.  =24)285.714(11  dwts.,  21f  grains  nearly,  weight  re- 
24  quired. 


45 
24 


21.714 

Required,  the  weight  of  1  Irish  or  Scotch  hank  of  number 
240's  yarn : — 


362  LIXEX  YARNS. 

Dividend. 

Numbers  of  yarn,  240)84! '00(350  grains,  Treiglit  required. 
720 


1200 
1200 


1  dwt.  =24  grns. 


2)350  grains. 


12)175 


14  dwts.,  14  grs.,  "weight  required. 

How  many  yards  are  there  in  1  Irish  or  Scotch  hank  of  yarn  ? 

300  yards,  1  lea,  or  cut. 
12  leas,  or  cuts,  are  1  Irish  or  Scotch  hank. 


3600  yards  in  1  Irish  or  Scotch  hank. 

Required,  the  weight  of  1  Irish  spangle  or  Scotch  spindle  of 
number  2G5's  yarn  : — 

Dividend. 

Numbers  of  yarn,  265)38000(1267.92  grains,  weight  required. 
265 

710 

530 

1800 
1590 

2100 

1855 

2450 
2885 

650 
530 

120 


LINEN  YARNS.  363 

Grains.  Grains. 
1  oz.  =437.5)1267.92(2  oz.,  16  dwts.,  9  grains  nearly,  weight 
875.0  required. 

1  dwt.  =24  grs.)392.92(16  dwts. 
24 


152 
144 


8.92  grains. 

How  many  yards  are  there  in  1  oz.  of  number  265's  yarn? 

265  numbers  of  yarn. 
300  yards,  1  lea  or  cut. 


(4)79500 

1  lb.  =16  oz.-l   

(4)19875 

4968.75,  or  4968f  yards  in  1  oz. 

Required,  the  weight  of  1  lea,  or  cut  of  number  298's  yarn? 

Dividend. 

Numbers  of  yarn,  298)7000(23.49,  or  23i  grains  nearly,  weight 
596  required. 

1040 
894 


1460 
1192 


2680 

2682— nearly. 

Required,  the  weight  of  1  English  bundle  of  number  295's 
yarn  : — 


364  LINEN  YARNS. 

Dividend. 

Numbers  of  yarn,  295)70000(237.288  grains,  weight  required. 

590 


1100 

885 


2150 
2065 


850 
690 


2600 
2360 


2400 
2360 


40 

1  dwt.  =  24  grains)2B7. 288(9  dwts.,21i  grains,  weight  required. 
216 


21.288  grains. 

How  many  yards  are  there  in  1  lb.  of  number  295's  yarn? 

295,  numbers  of  yarn. 
300  yards  in  1  lea  or  cut. 

88500  yards  in  1  lb.  of  number  295's  yarn. 

In  calculating  the  weight  of  linen  yarns  required  to  produce 
any  fabric  of  cloth,  the  rules  are  the  same  as  those  in  cotton, 
with  this  exception  only  :  300  yards  constitute  the  lea,  or  cut  in 
linen,  which  counts  in  the  numbers  of  yarn  the  same  as  840 
yards  in  cotton. 

What  will  the  weight  of  a  linen  warp  be,  124  yards  long,  con- 
taining 2160  ends  made  from  80's  yarn? 


LINEN  YARNS. 


365 


2160,  ends  in  the  warp. 
124 


8640 
4320 
2160 


1  lea  =3.00  yards)2678.40 


Numbers  of  yarn,  8.0)89.2.8 


11.16  lbs. 

16  oz.  are  1  lb. 


96 
16 


2.56  oz. 

4  qrs.,  1  oz. 


2.24  quarters. 
The  weight  of  the  warp  will  be  11  lbs.,  2  oz.,  2.24  qrs. 

If  a  warp  be  84  inches  wide  at  the  reed,  containing  2160  ends, 
how  many  ends  will  there  be  in  the  inch  ? 

34)2160(63.53,  or  63J  ends  in  an  inch  at 
204  the  reed. 


120 
102 


180 
170 


100 

102 — nearly. 

What  weight  of  number  95's  linen  yarn  will  it  require  to  weave 
a  warp  124  yards  long,  34  inches  wide,  and  76  picks,  or  threads 
in  an  inch? 


366 


LIXEN  TARNS. 


124  yards,  length  of  warp. 
34  inches,  width  of  warp  at  the 
  reed. 

496 
372 

4216 

76  picks,  or  threads  in  an  inch. 


25296 
29512 


1  lea  is  equal  to  3.00  yds.)8204.16 


Numhers  of  yarn,  95)1068.0533(11.2426  lbs. 

95  16  oz.  are  1  lb. 


118  14556 
95  2426 


230  3.8816 

190  4  qrs.  are  1  oz. 

405  3.5264,  or  11  lbs.,  3  oz., 

380  3J  qrs.  neat  weight 

  required  to  weave 

253  the  above. 
190 


633 
570 


63 

JV.  B. — Allowance  must  he  made  for  waste. 


The  length  and  weight  of  linen  yarns  required  for  manu- 
facturing any  fabric  of  linen  cloth,  may  be  ascertained  in  the 
same  manner  as  illustrated  in  the  two  preceding  examples. 


WORSTED  AND  WOOLLEN  YARNS. 


367 


WORSTED  AND  WOOLLEN  YARNS. 

All  worsted  and  woollen  yarns  being  sold  by  the  gross,  it  is 
necessary  that  the  manufacturer  of  worsted  and  woollen  pieces 
be  well  acquainted  with  the  weight  per  gross  according  to  the 
fineness  of  the  yarns,  in  order  to  insure  the  proper  weight  of  the 
piece  he  is  making.  The  yarn  being  too  heavy,  even  if  made 
from  wool  of  a  proper  quality,  gives  an  inferior  appearance. 

It  is  particularly  necessary  for  the  spinner  to  keep  a  strict 
check  upon  the  working  of  his  machinery;  wool  being  much 
sooner  affected  by  the  atmosphere  than  cotton. 

The  usual  plan  of  trying  the  fineness  of  worsted,  or  woollen 
yarns  is,  to  weigh  1  hank,  and  if  the  result  be  doubtful,  to  take 
a  quarter  of  a  gross  from  each  frame,  or  collectively,  as  circum- 
stances may  require. 

The  following  tables  will  show  the  weight  of  1  hank,  1  dozen, 
and  1  gross  of  worsted,  or  woollen  yarns,  from  number  1  to  270 
hanks  in  the  pound. 

If  the  weight  of  a  less  quantity  than  1  hank  should  be  re- 
quired, rules  and  examples  will  be  found  after  the  next  table. 

EXPLANATION  TO  THE  FOLLOWING  TABLES. 

The  first  and  last  columns  contain  the  numbers  or  counts  of 
yarn ;  opposite  to  which  in  the  table  is  the  weight  according  to 
the  lencrth  weighed. 

660  yards  make  1  hank, 
12  hanks  make  1  dozen. 
12  dozens,  or  144  hanks  make  1  gross. 

N.B. —  The  pounds  and  ounces  are  avoirdupois  weight;  the 
■pennyweights  and  grains  are  troy  weight. 

24  grains  are  equal  to  1  pennyweight. 

18  pennyweights,  5|-  grains  troy  are  equal  to  1  ounce  avoirdupois. 
16  ounces  are  equal  to  1  lb. 

Or, 

24  grains  make  1  pennyweight. 
437i^  grains  make  1  ounce  avoirdupois. 
7000  grains  make  1  pound  avoirdupois. 


368 


WORSTED  AND  WOOLLEN  TARNS. 


WORSTED  AND  WOOLLEN  YARN  TABLE. 


From  Number  1  to  40  hanks  in  the  pound. 


Weight  of  1  hanlf. 

Weight  of  1  dozen. 

1     Weight  of  1  gross. 

Nos. 

oz. 

dwts. 

1  grains. 

lbs. 

oz. 

dwts. 

1  grains. 

I  lbs. 

oz. 

dwts. 

grains. 

Nos. 

1 

16 

0 

0. 

12 

0 

0 



0. 

44 

0 

0 

0. 

1 

2 

8 

0 

0. 

6 

0 

0 

0. 

72 

0 

c 

0, 

2 

3 

5 

6 

1.8 

4 

0 

0 

0. 

48 

0 

0 

0. 

3 

4 

4 

0 

0. 

3 

0 

0 

0. 

36 

0 

0 

0. 

4 

5 

3 

3 

15.5 

2 

6 

7 

7. 

28 

12 

14 

14. 

5 

6 

2 

12 

3.6 

2 

0 

0 

0. 

24 

0 

0 

0. 

6 

7 

2 

5 

5. 

1 

11 

7 

19.5 

20 

9 

2 

14.5 

7 

8 

2 

0 

0. 

1 

8 

0 

0. 

18 

0 

0 

0. 

8 

9 

1 

14 

4.2 

1 

5 

6 

1.8 

16 

0 

0 

0. 

9 

10 

1 

10 

22.5 

1 

3 

3 

15.5 

14 

6 

7 

7. 

10 

11 

1 

8 

6.8 

1 

1 

8 

6.8 

13 

1 

8 

6. 

11 

12 

1 

6 

1.8 

1 

0 

0 

0. 

12 

0 

0 

0. 

12 

13 

1 

4 

4.9 

14 

14 

0.5 

11 

1 

4 

4.9 

13 

14 

1 

2 

14.5 

13 

13 

0.5 

10 

4 

10 

10. 

14 

15 

1 

1 

5.1 

12 

14 

14. 

9 

9 

10 

22.5 

15 

16 

1 

0 

0. 

12 

0 

0. 

9 

0 

0 

0. 

16 

17 

17 

3.7 

11 

5 

8.6 

8 

7 

9 

15.6 

17 

18 

16 

4.8 

10 

12 

3.6 

8 

0 

0 

0. 

18 

19 

15 

8.4 

10 

1 

22. 

7 

9 

4 

19.1 

19 

20 

14 

14. 

9 

10 

22.5 

7 

3 

3 

15.5 

20 

21 

13 

21.3 

9 

2 

14.5 

6 

13 

13 

0.5 

21 

22 

13 

6.1 

8 

13 

6.1 

6 

8 

13 

5.75 

22 

23 

12 

16.3 

8 

6 

8.1 

6 

4 

3 

4. 

23 

24 

12 

3.6 

8 

0 

0. 

6 

0 

0 

0. 

24 

25 

11 

16. 

7 

12 

9.5 

5 

12 

2 

22. 

25 

26 

11 

5.2 

7 

7 

0.2 

5 

8 

11 

5.2 

26 

27 

10 

19.2 

7 

2 

0.6 

5 

5 

6 

1.8 

27 

28 

10 

10, 

6 

15 

15. 

5 

2 

5 

5. 

28 

29 

10 

1.3 

6 

1 1 

7.5 

4 

ID 

o 
O 

4. 1 

29 

30 

9 

17.3 

6 

7 

7. 

4 

12 

14 

14. 

30 

Q  1 
O  1 

9 

9.8 

6 

3 

12.6 

4 

10 

5 

21.1 

32 

9 

2.7 

6 

0 

0. 

4 

8 

0 

0. 

32 

33 

8 

20.1 

5 

14 

21.9 

4 

5 

14 

21.6 

33 

34 

8 

13.8 

5 

11 

19. 

4 

3 

13 

22.5 

34 

35 

8 

7.9 

8 

20.5 

4 

1 

15 

2.5 

35 

36 

8 

2.4 

I 

6 

1.8 

4 

0 

0 

0. 

38 

37 

7 

21.1 

5 

3 

10.7 

3 

14 

4 

22.2 

37 

38 

7 

16.2 

5 

0 

23. 

3 

12 

11 

12.3 

38 

39 

7 

11.4 

4 

16 

19.8 

3 

]  1 

1 

14.45 

39 

40 

7 

7. 

4 

14 

14. 

3 

9 

10 

22.5 

40 

WORSTED  AND  WOOLLEN  YARNS. 


369 


If  the  weight  of  any  shorter  length  than  stated  in  the  pre- 
ceding table  should  be  required,  it  may  be  ascertained  by  taking 
the  number  opposite  the  length  weighed  as  shown  below  for  a 
dividend,  and  the  numbers,  or  counts  of  yarn  for  a  divisor,  and 
the  quotient  will  be  the  weight  in  grains;  or,  take  the  number  of 
grains  any  given  length  weighs  for  a  divisor,  and  the  number 
opposite  that  given  length  for  a  dividend,  and  the  quotient  will 
be  the  numbers,  or  counts  of  yarn  roving,  &c. 

Given  lengths. 


Yards.  Dividends. 

1  gross,  or  80640  10U8000 

1  dozen,  or  6720  84000 

1  hank,  or  560  7000 
6  leas,  or  480  6000 
5  leas,  or  400  5000 
4  leas,  or  820  4000 
3  leas,  or  240  8000 

2  leas,  or  160  2000 
1  lea,  or  80  1000 
I  lea,  or  60  750 
I  lea,  or  40  500 
i  lea,  or  20  250 
1  lea,  or  10  125 
y'g  lea,  or  5  62.5 
4'o  lea,  or  2  25 
g'o  lea,  or  1  12.5 


H.B. —  The  ivorsfcd  reel  is  2  yards  in  circumference,  and  40 
threads  round  the  reel  make  1  lea,  and  7  leas  make  1  hank. 

Required  the  weight  of  40  yards  of  a  hank  roving : — 

Look  opposite  40  yards  in  the  above  table,  and  you  will  find 
500,  which  is  the  dividend,  and  divide  by  4,  the  numbers,  or 
counts  of  roving,  and  the  quotient  will  be  the  weight  in  grains. 

Numbers,  or  counts  of  roving,  4  hanks)500  dividend. 

125  grains,  or  5  penny- 
weights, 5  grains, 
weight  required. 


70  WORSTED  AND  WOOLLEN  YARNS. 

WORSTED  AND  WOOLLEN  YARN  TABLE. 


From  Number  41  to  80  hanks  in  the  pound. 


Wght.  of  1  hnk. 

Weight  of  1  dozen. 

1        Weight  of  1  gross. 

Nos. 

Midi  llOa 

oz. 

grsiDs. 

lbs. 

OZ. 

d  w  ts. 

grain!.. 

Nos. 

41 

7 

2.7 

4 

12 

10.7 

3 

8 

3 

13.3 

41 

42 

6 

22.6 

4 

10 

10. 

3 

6 

15 

15. 

42 

43 

6 

18.7 

4 

8 

11.4 

3 

5 

10 

14.3 

43 

44 

6 

15. 

4 

6 

15.1 

3 

4 

6 

14.8 

44 

45 

6 

11.5 

4 

4 

20.6 

3 

3 

3 

15.5 

45 

46 

6 

8.1 

4 

3 

4. 

3 

2 

1 

14. 

46 

47 

6 

4.9 

4 

1 

13.2 

3 

1 

0 

9.3 

47 

48 

6 

1.8 

4 

0 

0. 

3 

0 

0 

0. 

48 

49 

5 

22.8 

3 

16 

17.7 

2 

15 

0 

8.9 

49 

50 

5 

20. 

3 

15 

7.5 

2 

14 

1 

11. 

50 

51 

5 

17.2 

3 

13 

22.5 

2 

13 

3 

5.2 

51 

52 

5 

14.6 

3 

12 

14.8 

2 

12 

5 

14.6 

52 

53 

5 

12. 

3 

11 

8.4 

2 

11 

8 

14.3 

53 

54 

5 

9.6 

3 

10 

3. 

2 

10 

12 

15.6 

54 

55 

5 

7.2 

3 

8 

22.7 

2 

9 

16 

5.7 

55 

56 

5 

5. 

3 

7 

19.5 

2 

9 

2 

14.5 

56 

57 

5 

2.8 

3 

6 

17.1 

2 

8 

7 

16.2 

57 

58 

5 

0.6 

3 

5 

15.7 

2 

7 

13 

4.8 

58 

59 

4 

22.6 

3 

4 

15.2 

2 

7 

0 

22.2 

59 

60 

4 

20.6 

3 

3 

15.5 

2 

6 

7 

7. 

60 

61 

4 

18.7 

3 

2 

16.5 

2 

5 

14 

0.1 

61 

62 

4 

16.9 

3 

1 

18.3 

2 

5 

2 

22.5 

62 

63 

4 

15.1 

3 

0 

20.8 

2 

4 

10 

lo. 

63 

64 

4 

13.3 

3 

0 

0. 

2 

4 

0 

0. 

64 

65 

4 

11.6 

2 

17 

9.3 

2 

3 

8 

3.2 

65 

66 

4 

10. 

2 

16 

13.7 

2 

2 

16 

13.7 

66 

67 

4 

8.4 

2 

15 

18.7 

2 

2 

17 

1.7 

67 

68 

4 

6.9 

2 

15 

0.3 

2 

1 

16 

2. 

66 

69 

4 

5.4 

2 

14 

6.4 

2 

1 

7 

3.2 

69 

70 

4 

4. 

2 

13 

13. 

2 

0 

16 

16. 

70 

71 

4 

2.6 

2 

12 

20.1 

2 

0 

8 

5.1 

71 

72 

4 

1.2 

2 

12 

3.6 

2 

0 

0 

0. 

72 

73 

3 

23.9 

2 

11 

11.6 

15 

10 

5.7 

73 

74 

3 

22.6 

2 

10 

20.1 

15 

2 

11.1 

74 

75 

3 

21.3 

2 

10 

5. 

14 

13 

3. 

75 

76 

3 

20.1 

2 

9 

14.2 

14 

5 

18.1 

76 

77 

3 

18.9 

2 

8 

23.9 

13 

16 

19.4 

77 

78 

3 

17.7 

2 

8 

9.9 

13 

9 

19.5 

78 

79 

3 

16.6 

2 

7 

20.3 

13 

3 

0. 

79 

80 

3 

15.5 

2 

7 

7. 

12 

14 

14. 

80 

WORSTED  AND  WOOLLEN  YARNS. 


371 


Required,  the  weight  of  1  lea  of  number  36's  yarn: — 
Look  opposite  1  lea,  or  80  yards,  and  you  will  find  1000  which 

is  the  dividend,  the  numbers  of  yarn,2.  e.,  36's  will  be  the  divisor, 

and  the  quotient  will  be  the  weight  in  grains. 
Dividend. 

Numbers  of  yarn,  36's)1000(27.77  grains,  or  1  dwt.,  3f  grains, 
72  weiglat  required. 


280 
252 


280 
252 


280 
252 

28 

If  1  lea,  or  80  yards  of  yarn  weigh  27.77  grains;  what  num- 
bers, or  counts  will  it  be? 

1000  is  the  dividend  for  1  lea,  or  80  yards. 
Weight  of  1  lea,  27.77  grs.)1000.00(36,  numbers,  or  counts  of 

8333  yarn. 


16666 
16666 

Required,  the  weight  of  1  hank  of  number  80's  yarn:  — 
7000  is  the  dividend  for  1  hank,  or  560  yards. 
Numbers  of  yarn,  8.0)700.0 

87.5  grains,  or  3  dwts.,  15^  grains  weight 

required. 

If  1  hank,  or  560  yards,  weigh  3  dwts.,  15J  grains,  or  87.5 
grains;  what  numbers  Avill  it  be? 

7000  is  the  dividend  for  1  hank,  or  560  yards. 
Weight  of  1  hk.  87.5  grs.)7 000.0(80,  number  of  counts  of  yarn. 

7000 


0 

I^.  B. —  77ie  above  examples  luill  he  sufficient  to  illustrate  the 
tables;  but  if  more  should  be  required,  see  cotton^  the  only 
difference  being  the  length  constituting  the  hank. 


372 


WORSTED  AXD  WOOLLEN  TARNS. 


WORSTED  AND  WOOLLEN  YARNS. 


From  Number  80  to  120  hanks  in  the  pound. 


Wo-t 
\  \  I 

nf  1  hk. 

1 

1  Weight  of  1  dozen. 

Weight  of  1  gross.  | 

^  r<iin  s . 

oz. 

d  wts. 

grains. 

iOS. 

oz. 

1  dwts. 

grains. 

Nos. 

81 

3 

14.4 

2 

5 

18. 

Q 

O 

9  4 

1 

0  I 

82 

3 

13.3 

2 

5 

5.4 

12 

1  R  R 
X  o .  u 

ft  9 

83 

3 

12.3 

5 

1 7 

X  . 

\  \ 

X  t> 

90 

00 

84 

3 

11.3 

2 

5 

5. 

1 1 

1  X 

7 

90  ^ 

At\JtO 

ft  J. 

85 

3 

10.3 

2 

4 

1  7  2 

1 1 

X  X 

1 
X 

99 

ft  ^ 

86 

3 

9.4 

9 

4 

7 

1  0 

X  \J 

X  ^ 

Q  Q 

Rfi 
00 

87 

3 

8.4 

9 

Q 

1  8  'S 

1  0 

X  \J 

Q 
O 

1  Q  9 

ft7 

88 

3 

7.5 

2 

Q 

7  5 

1 

1  0 

X  \J 

q 
o 

7 

ftft 

89 

3 

6.6 

9 

9 

Q 

4  Q 

ftq 

90 

3 

5.7 

9 

9 

1  fl 
X  w .  o 

q 

1  0 

X  \J 

99 

qq 

91 

3 

4.9 

9 

9 

0 

q 

1  Q  4 

q  1 

92 

3 

4. 

9 

1 

1  i. 

X  T-  . 

q 

u 

1  Q 
X  «7. 

Q9 

93 

3 

3.2 

9 

1 

Q 
O 

1  J. 

9  7 

qQ 
yo 

94 

3 

2.4 

9 

u 

X  o .  u 

Q 

o 

q 

7  4 

q/t 

95 

3 

1.6 

9 

0 

Q  '2 

Q 
O 

/I 

1  4 
X  4:.  t> 

qf^ 
y  t) 

96 

3 

0.9 

9 

u 

0 

\J . 

Q 
O 

n 

U 

n 

U. 

qfi 
y  0 

97 

3 

0.1 

1 1 

90  4 

/ 

X  t> 

1  7  9 

q7 
y  / 

98 

2 

23.4 

1  7 

X  i 

1  1  R 

X  X  .  LI 

-. 

/ 

q 

7  9 

qft 
y  0 

99 

2 

22.7 

1  7 
X  / 

9  Q 

7 

J. 

9^  ^ 

qq 
y  y 

100 

2 

22. 

1  R 
X  u 

18.5 

- 

7 

0 

10. 

1  no 

101 

2 

21.3 

1  6 
X  u 

10. 1 

fl 
u 

14 

X  ^ 

14  1 

102 

2 

20.6 

X  \J 

9 

A 

\j 

X  f 

17^ 
X  /  .0 

1  09 

103 

2 

19.9 

X 

X  o . 

fl 

u 

fl 
t) 

17  4 

X  /.4r 

1  HQ 

104 

2 

19.3 

X  u 

10.2 

fl 
u 

9 

X  €7.  0 

1  qj. 

105 

2 

18.6 

1 

X  u 

9 

o 

1  7 

4  fi 

1  n  ^ 
1  u«> 

106 

2 

18. 

1  4 
X  ^ 

1  ^ 
1  »5 

Q  Q 

1  OA 

107 

2 

17.4 

14 

11.5 

5 

9 

17. 

107 

108 

2 

16.8 

; 

14 

4.2 

5 

6 

1.8 

108 

109 

2 

16.2 

13 

21.1 

5 

2 

12.2 

109 

110 

2 

15.6 

13 

14.1 

4 

17 

5.6 

110 

111 

2 

15. 

13 

7.2 

4 

13 

19. 

111 

112 

2 

14.5 

13 

0.5 

4 

10 

10. 

112 

113 

2 

13.9 

12 

17.8 

4 

7 

2.3 

113 

114 

2 

13.4 

12 

11.3 

4 

3 

20.1 

114 

115 

2 

12.8 

12 

4.9 

4 

0 

15.2 

115 

116 

2 

12.3 

11 

22.0 

3 

15 

17.1 

116 

117 

2 

11.8 

11 

16.4 

3 

12 

14.8 

117 

118 

2 

11.3 

11 

10.3 

3 

9 

13.8 

118 

119 

2 

10.8 

11 

4.3 

3 

6 

14. 

119 

120 

2 

10.3 

10 

22.5 

3 

3 

15.5 

120 

WORSTED  AND  WOOLLEN  YARNS.  373 

Required,  the  length  and  weight  of  number  56's  yarn,  for  a 
warp  128  yards  long,  3G  inches  wide  at  the  reed,  and  to  have 
84  threads  in  an  inch: —  , 

128  yards,  length  of  warp, 
36  inches,  width  of  warp  at  the  reed. 

768 
384 


4608 

84,  threads  in  an  inch. 


18432 
36864 


387072,  total  No.  of  yds.  of  yarn  in  the  warp. 
Yards. 

1  gross  contains  80640  yd3.)387072(4  gross. 

322560 


1  dozen  contains  6720  yds.)64512(9  dozen. 

60480 


1  hank  contains  560  yd8.)4032(7  hanks. 

3920 


1  lea  contains  80  yds.)112(l  lea. 

80 


1  thread  contains  2  yds.)32 


'16  threads. 

The  length  of  yarn  required  for  the  above  warp  will  be  4  gross, 
9  dozen,  7  hanks,  1  lea,  and  16  threads. 

560  yards,  1  hank. 
66,  numbers  of  yarn. 

3360 
2800 


31360  number  of  yards  in  1  lb.,  of  56's  yarn. 


374 


WORSTED  AND  WOOLLEN  YARNS. 


WORSTED  AND  WOOLLEN  YARN  TABLE. 


From  Number  121  to  160  hanks  in  tlie  pound. 


Wght.  of]  hnk. 

Wei 

ght  of  1  dozen. 

Weight  of  1  gross. 

Nos. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

Nos. 

121 

2 

9.8 

1 

10 

16.7 

1 

8 

0 

18. 

121 

122 

2 

9.3 

1 

10 

11. 

1 

2 

16 

8.8 

122 

123 

2 

8.9 

1 

10 

5.4 

1 

2 

18 

8.1 

123 

124 

2 

8.4 

1 

9 

23.9 

1 

2 

10 

5.9 

124 

125 

2 

8. 

i 

9 

18.5 

1 

2 

7 

21. 

125 

12(3 

2 

7.5 

i 

9 

13.1 

1 

2 

5 

5. 

126 

127 

2 

7.1 

i 

9 

7.9 

1 

2 

2 

14. 

127 

128 

2 

6.6 

1 

9 

2.7 

1 

2 

0 

0. 

128 

129 

2 

6.2 

1 

8 

21.6 

1 

1 

15 

16.4 

129 

130 

2 

5.8 

i 

8 

16.6 

1 

1 

18 

4.3 

130 

131 

•  2 

5.4 

-t 
1 

8 

11.7 

1 

1 

10 

17.1 

131 

132 

2 

5. 

-t 
i 

8 

6.8 

1 

1 

8 

6.8 

132 

133 

2 

4.6 

-t 
1 

8 

0 

1 

1 

5 

20.7 

133 

134 

2 

4.2 

-1 
1 

7 

21.8 

1 

1 

3 

12.8 

134 

loo 

2 

3.8 

i 

7 

16.7 

1 

1 

1 

5.1 

135 

16b 

2 

3.4 

1 

7 

12.1 

1 

0 

17 

8.7 

136 

13/ 

2 

3.1 

-t 
1 

7 

7.6 

1 

0 

14 

21.6 

187 

138 

2 

2.7 

1 

7 

8.2 

1 

0 

12 

16.3 

138 

loy 

f) 

2.3 

1 

6 

22.8 

1 

0 

10 

11.8 

139 

140 

2 

o 

i 

6 

18.5 

1 

0 

8 

8. 

140 

141 

2 

1.6 

1 

1 

6 

14.2 

1 

0 

6 

4.9 

141 

142 

1.3 

1 

6 

10. 

1 

0 

4 

2.5 

142 

14o 

o 

1. 

1 

6 

5.9 

1 

0 

2 

0.9 

143 

144 

2 

0.6 

1 

6 

1.8 

1 

0 

0 

0. 

144 

14o 

- 

0.2 

1 

5 

21.8 

15 

16 

5.2 

145 

l4b 

1 

23.9 

1 

5 

17.8 

15 

14 

5.6 

146 

147 

1 

23.6 

1 

5 

18.9 

15 

12 

6.6 

147 

148 

1 

23.3 

1 

5 

10. 

15 

10 

8.3 

148 

149 

1 

23. 

1 

5 

6.2 

15 

8 

10.6 

149 

150 

1 

22.6 

1 

5 

2.5 

15 

6 

18.5 

150 

151 

1 

22.3 

1 

4 

22.8 

15 

4 

16.9 

151 

152 

1 

22. 

1 

4 

19.1 

15 

2 

21. 

152 

153 

1 

21.7 

1 

4 

15.5 

15 

1 

1.7 

153 

154 

1 

21.4 

1 

4 

11.9 

14 

17 

12.4 

154 

155 

1 

21.1 

1 

4 

8.4 

14 

15 

18.8 

155 

156 

1 

20.8 

1 

4 

4.9 

14 

14 

0.5 

156 

157 

1 

20.5 

1 

4 

1.5 

14 

12 

7.8 

157 

158 

1 

20.3 

1 

3 

22.1 

14 

10 

14.7 

158 

159 

1 

20. 

1 

3 

18.8 

14 

8 

22.6 

159 

160 

1 

19.7 

1 

3 

15.5 

14 

7 

7. 

160 

WORSTED  AND  WOOLLEN  TARNS.  375 

Yards.  Yards  in  the  warp. 
1  lb.  of  No.  56's  =31360)387072(12.34  lbs.,  or  12  lbs.,  5h  oz. 

31360        16  oz.,  1  lb. 


73472 

204 

62720 

34 

107520 

5.44 

94080 

4 

1344001.76  qrs. 
125440-8960,  remainder. 

The  weight  of  yarn  required  for  the  above  warp  will  be  12 
lbs.,  5J  oz.  nearly. 

Required,  the  weight  of  number  66's  yarn,  to  weave  a  warp 
128  yards  long,  36  inches  Avide  at  the  reed,  and  to  have  88  picks, 
or  threads  in  an  inch  : — 

128  yards,  length  of  warp. 
36  inches,  width  of  warp  at  the  reed. 

768 

384 


4608 

88,  number  of  picks,  or  threads  in  an  inch. 


36864 
36864 


405504  No.  of  yds.  of  yarn  required  to  weave 

the  warp. 

Yards.  Yards. 

1  gross  contains  80640)405504(5  gross,  4  hanks,  and  32  threads, 
403200         length  of  yarn  required  to 

  Aveave  the  warp. 

1  hank  contains  560  yds.)2304(4  hanks. 

2240 


1  thread  contains  2  yards,)64 

32  threads. 


376  WORSTED  AXD  WOOLLEN  YARNS. 

560  yards,  1  hank. 
66,  numbers  of  yarn. 


8360 
3360 


36960,  number  of  yards  in  1  lb.  of  66's  yarn. 


4 


WORSTED  AND  WOOLLEN  YARNS. 


377 


WORSTED  AND  WOOLLEN  YARN  TABLE. 


From  Number  161  to  200  hanks  in  the  pound. 


Weight  of  1  hank. 

Weight  of  1  dozen. 

Weight  of  1 

gross. 

Nos. 

d  wt. 

lbs. 

d  vv  ts . 

grains. 

lbs. 

grams. 

161 

1 

19.4 

1 

3 

12.2 

14 

5 

15.8 

161 

162 

1 

19.2 

1 

3 

9. 

14 

4 

1.2 

162 

163 

1 

18.9 

1 

8 

5.8 

14 

2 

11. 

168 

164 

1 

18.6 

1 

3 

2.7 

14 

0 

21.3 

164 

165 

1 

18.4 

1 

2 

23.6 

13 

17 

13.6 

165 

166 

1 

18.1 

1 

2 

20.5 

13' 

16 

0.7 

166 

167 

1 

17.9 

1 

2 

17.5 

13 

14 

12.4 

167 

168 

1 

17.6 

1 

2 

14.5 

13 

13 

0.5 

168 

169 

1 

17.4 

1 

2 

11.5 

13 

11 

18. 

169 

170 

1 

17.1 

1 

2 

8.6 

13 

10 

1.9 

170 

171 

1 

16.9 

1 

2 

5.7 

13 

8 

15.2 

171 

172 

1 

16.7 

1 

2 

2.8 

13 

7 

4.9 

172 

173 

1 

16.4 

1 

2 

0. 

13 

5 

19. 

178 

174 

1 

16.2 

1 

1 

21.2 

13 

4 

9.6 

174 

175 

1 

16. 

1 

1 

18.5 

13 

3 

0.5 

175 

176 

1 

15.7 

1 

1 

15.7 

13 

1 

15.7 

176 

177 

1 

15.5 

1 

1 

13. 

13 

0 

7.4 

177 

178 

1 

15.3 

1 

1 

10.4 

12 

17 

4.9 

178 

179 

1 

15.1 

1 

1 

7.7 

12 

15 

21.2 

179 

180 

1 

14.8 

1 

1 

5.1 

12 

14 

14. 

180 

181 

1 

14.6 

1 

1 

2.5 

12 

18 

7. 

181 

182 

1 

14.5 

1 

1 

0. 

12 

12 

0.4 

182 

188 

1 

14.2 

1 

0 

21.5 

12 

10 

18.1 

183 

184 

1 

14. 

1 

0 

19. 

12 

9 

12.2 

184 

185 

1 

13.8 

1 

0 

16.5 

12 

8 

6.6 

185 

186 

1 

13.6 

1 

0 

14.1 

12 

7 

1.3 

186 

187 

1 

13.4 

1 

0 

11.7 

12 

5 

20.3 

187 

188 

1 

13.2 

1 

0 

9.3 

12 

4 

15.7 

188 

189 

1 

13. 

1 

0 

6.9 

12 

8 

11.3 

189 

190 

1 

12.8 

1 

0 

4.6 

12 

2 

7.2 

190 

191 

1 

12.6 

1 

0 

2.3 

12 

1 

3.4 

191 

192 

1 

12.4 

1 

0 

0. 

12 

0 

0. 

192 

193 

1 

12.2 

18 

8.2 

11 

17 

2.3 

193 

194 

1 

12. 

18 

0.9 

11 

15 

23.3 

194 

195 

1 

11.8 

17 

22.7 

11 

14 

20.7 

195 

196 

1 

11.7 

17 

2o!5 

11 

18 

18.3 

196 

197 

1 

11.5 

17 

18.4 

11 

12 

16.2 

197 

198 

1 

11.3 

17 

16.2 

11 

11 

14.4 

198 

199 

1 

11.1 

17 

14.1 

11 

10 

12.8 

199 

200 

1 

11. 

17 

12. 

11 

9 

11.5 

200 

25 


378 


WORSTED  AND  WOOLLEN  TARNS. 


Yards.  Yards  in  the  warp. 
1  lb.  of  No.  66's  =  36960)405504(10  lbs.,  15i  oz.,  wt.  of  weft  re- 

36960         quired  to  weave  the  warp. 


35904 

16  oz.  1  lb. 


215424 
35904 


36960)574464(15  oz. 
36960 


204864 
184800 


20064 

4  qrs,,  1  oz. 


36960)80256(2  qrs. 
73920 


6336 

If  it  requires  12  lbs.,  5J  oz.  of  yarn  for  a  warp,  and  10  lbs., 
15|-  0^.  of  yarn  to  weave  the  -v^rp ;  what  weight  will  it  require 
for  1  piece,  if  there  be  4  pieces  in  the  warp? 

lbs.  oz. 

12  .  .   5f,  weight  of  the  warp. 

10  .  .  15J,  weight  to  Aveave  the  warp. 


No.  of  pieces  in  warp,  4)23  .  .  5 


5  .  .  13J,  weight  of  1  piece. 

jy.  B. —  The  rules,  examples,  and  illustrations  laid  doivn  for  the 
manufacture  of  cotton  goods,  may  he  applied  to  the  manufac- 
ture of  any  other  fabric  of  cloth,  such  as  linen,  worsted,  ivoollen, 
or  silk ;  the  system  of  calculation  being  the  same,  with  the  ex- 
ception of  the  length  constituting  the  lea  and  hank,  all  particu- 
lars of  which  will  be  found  in  their  proper  places  in  this  book. 


WORSTED  AND  WOOLLEN  YARNS.         , -.  -3^9 


WORSTED  AND  WOOLLEN  YARN  TABLE. '  -'X/^,  p 
From  Number  201  to  270  hanks  in  the  pound. 


Wgt.  of  1  hank. 

Weight  of  1  dozen. 

Weight  of  1  gross. 

Nos. 

dwts. 

grains. 

oz. 

dwts. 

grains. 

lbs. 

oz. 

dwts. 

grains. 

Noe. 

201 

1 

10.8 

17 

9.9 

11 

8 

10.4 

201 

202 

1 

10.6 

17 

7.8 

11 

7 

9.6 

202 

203 

1 

10.4 

17 

5.8 

11 

6 

9. 

203 

204 

1 

10.3 

17 

3.7 

11 

5 

8.6 

204 

205 

1 

10.1 

17 

1.7 

11 

4 

8.5 

205 

206 

1 

9.9 

16 

23.7 

11 

3 

8.7 

206 

207 

1 

9.8 

16 

21.8 

11 

2 

9. 

207 

208 

1 

9.6 

16 

19.8 

11 

1 

9.6 

208 

209 

1 

9.4 

16 

17.9 

11 

0 

10.4 

209 

210 

1 

9.3 

16 

16. 

10 

17 

17. 

210 

211 

1 

9.1 

16 

14.1 

10 

16 

18.2 

211 

212 

1 

9. 

16 

12.2 

10 

15 

19.7 

213 

1 

8.8 

16 

10.3 

10 

14 

21.3 

213 

214 

1 

8.7 

16 

8.5 

10 

13 

23.2 

214 

215 

1 

8.5 

16 

6.7 

10 

13 

1.3 

215 

216 

1 

8.4 

16 

4.8 

10 

12 

3.6 

216 

217 

1 

8.2 

16 

3.1 

10 

11 

6.1 

217 

218 

1 

8.1 

16 

1.3 

10 

10 

8.8 

218 

219 

1 

7.9 

15 

23.5 

10 

9 

11.7 

219 

220 

1 

7.8 

15 

21.8 

10 

8 

14.8 

220 

221 

1  1 

7.6 

15 

20.1 

10 

7 

18. 

221 

222 

1 

7.5 

15 

18.3 

10 

6 

21.5 

222 

223 

1 

7.3 

15 

16.6 

10 

6 

1.1 

223 

2.1\ 

1 

7.2 

15 

15. 

10 

5 

5. 

224 

225 

1 

7.1 

15 

13.3 

10 

4 

9. 

225 

226 

1 

6.9 

15 

11.6 

10 

3 

13.1 

226 

/~j  O  T 

227 

1 

6.8 

15 

10. 

10 

2 

17.5 

227 

228 

1 

6.7 

15 

8.4 

10 

1 

22. 

228 

229 

1 

6.5 

15 

6.8 

10 

1 

2.7 

229 

230 

1 

6.4 

15 

5.2 

10 

0 

7.6 

230 

231 

1 

6.3 

15 

3.6 

9 

17 

18.1 

231 

232 

1 

6.1 

15 

2. 

9 

16 

23.3 

232 

235 

1 

5.7 

14 

21.4 

9 

14 

15.8 

235 

240 

1 

5.1 

14 

14. 

9 

10 

22.5 

240 

245 

1 

4.5 

14 

6.8 

9 

7 

8.7 

245 

250 

1 

4. 

14 

0. 

9 

3 

22.5 

250 

255 

1 

3.4 

13 

17.4 

9 

0 

15.4 

255 

260 

1 

2.9 

13 

11. 

8 

15 

16.9 

260 

265 

1 

2.4 

13 

5. 

8 

12 

15.7 

265 

270 

1 

1.9 

12 

23.1 

8 

9 

17.3 

270 

380  WORSTED  REEDS. 


WORSTED  COUNT  OF  REEDS. 

The  following  are  the  general  acknowledged  methods  of 
counting  and  expressing  reeds  in  the  manufacturing  of  all 
worsted  goods. 

1st.  The  plain  back,  or  three  ends  in  a  dent,  the  counts,  or 
fineness  of  the  set,  which  is  expressed  by  the  number  of  scores, 
or  beers,  20  dents  to  a  beer  set  on  6-4ths,  or  54  inches  at  the 
reed.  Thus,  a  42  contains  42  scores,  or  42  beers,  20  dents  to  a 
beer,  or  840  dents  on  54  inches  at  the  reed. 

iV.  B. —  This  reed  is  the  viost  common  one  in  use  at  the  present 
time. 

2d.  The  wildbore,  or  4  ends  in  a  dent,  the  count,  or  fineness 
of  the  set,  which  is  expressed  by  the  number  of  scores,  or  beers, 
20  dents  to  a  beer,  set  on  8-4ths,  or  72  inches  at  the  reed. 
Thus,  a  50  wildbore  slaie,  or  reed,  contains  50  scores,  or  60 
beers,  20  dents  to  a  beer,  or  1000  dents  on  72  inches  at  the  reed. 

B. —  This  method  is  very  little  in  use  now. 

3d.  The  2  ends  in  a  dent  is  coming  more  into  use,  the  fineness 
of  the  set,  which  is  expressed  by  the  number  of  scores,  or  beers, 
20  dents  to  a  beer  set  on  4-4ths  or  36  inches  at  the  reed. 

4th.  Lastings.  The  count,  or  fineness  of  the  set,  which  is  ex- 
pressed by  the  number  of  dents  set  on  30  inches  at  the  reed. 
Thus  a  4  contains  400  dents,  a  4  J  contains  450  dents,  &c.  &c. 

The  following  tables  will  show  the  count,  or  fineness  of  worsted 
reeds,  according  to  the  number  of  dents  in  an  inch,  and  the 
difi'erent  systems  of  counting. 

EXPLANATION  TO  THE  REED  TABLES. 

The  first  line  in  each  division  contains  the  number  of  dents  in 
an  inch ;  opposite  to  which  in  the  table  is  the  count  of  the  reed, 
according  to  the  different  systems  of  counting. 

N.  B. —  The  decimal  in  the  line  expressing  the  number  of  dents 
in  an  inch,  is  the  decimal  of  a  dent.  Thus,  20.5  is  equal  to 
20J  dents,  and  the  decimal  in  the  lines  expressing  the  counts 
of  the  reeds,  is  the  decimal  of  a  score,  or  beer  containing  20 
dents.    Thus,  40.5  is  equal  to  40J  scores,  or  beers. 


WORSTED  REEDS.  381 


WORSTED  REED  TABLE. 


c  . 

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8. 

21.6 

28.8 

14.4 

240 

25.5 

68.85 

91.8 

45.9 

765 

8.5 

22.95 

30.6 

15.3 

255 

26. 

70.2 

93.6 

46.8 

780 

9. 

24.3 

32.4 

16.2 

270 

26.5 

71.55 

95.4 

47.7 

795 

9.5 

25.65 

34.2 

17.1 

285 

27. 

72.9 

97.2 

48.6 

810 

10. 

27.. 

36. 

18. 

800 

27.5 

74.25 

99. 

49.5 

825 

10.5 

28.35 

37.8 

18.9 

315 

28. 

75.6 

100.8 

50.4 

840 

11. 

29.7 

39.6 

19.8 

330 

28.5 

76.95 

102.6 

51.3 

855 

11.5 

31.05 

41.4 

20.7 

345 

29. 

78.3 

104.4 

52.2 

870 

12. 

32.4 

43.2 

21.6 

360 

29.5 

79.65 

106.2 

53.1 

885 

12.5 

33.75 

45. 

22.5 

375 

30. 

81. 

108. 

54. 

900 

13. 

35.1 

46.8 

23.4 

390 

30.5 

82.35 

109.8 

54.9 

915 

13.5 

36.45 

48.6 

24.3 

405 

31. 

83.7 

111.6 

55.8 

930 

14. 

37.8 

50.4 

25.2 

420 

31.5 

85.05 

113.4 

56.7 

945 

14.5 

39.15 

52.2 

26.1 

435 

32. 

86.4 

115.2 

57.6 

960 

15. 

40.5 

54. 

27. 

450 

32.5 

87.75 

117. 

58.5 

975 

15.5 

41.85 

55.8 

27.9 

465 

33. 

89.1 

118.8 

59.4 

990 

16. 

43.2 

57.6 

28.8 

480 

33.5 

90.45 

120.6 

60.3 

1005 

16.5 

44.55 

59.4 

29.7 

495 

34. 

91.8 

122.4 

61.2 

1020 

17. 

45.9 

61.2 

30.6 

510 

34.5 

93.15 

124.2 

62.1 

1035 

17.5 

47.25 

63. 

31.5 

525 

35. 

94.5 

126. 

63. 

1050 

18. 

48.6 

64.8 

32.4 

540 

35.5 

95.85 

127.8 

63.9 

1065 

18.5 

49.95 

6G.6 

33.3 

555 

36. 

97.2 

129.6 

64.8 

1080 

19. 

51.3 

68.4 

34.2 

570 

36.5 

98.55 

131.4 

65.7 

1095 

19.5 

52.65 

70.2 

35.1 

585 

37. 

99.9 

133.2 

66.6 

1110 

20. 

54. 

72. 

36. 

600 

37.5 

101.25 

135. 

67.5 

1125 

20.5 

55.35 

73.8 

36.9 

615 

38. 

102.6 

136.8 

68.4 

1140 

21. 

56.7 

75.6 

37.8 

630 

38.5 

103.95 

138.6 

69.3 

1155 

21.5 

58.05 

77.4 

38.7 

645 

39. 

105.3 

140.4 

70.2 

1170 

22. 

59.4 

79.2 

39.6 

660 

39.5 

106.65 

142.2 

71.1 

1185 

22.5 

60.75 

81. 

40.5 

675 

40. 

108. 

144. 

72. 

1200 

23. 

62.1 

82.8 

41.4 

690 

40.5 

109.35 

145.8 

72.9 

1215 

23.5 

63.45 

84.6 

42.3 

705 

41. 

110.7 

147.6 

73.8 

1230 

24. 

64.8 

86.4 

43.2 

720 

41.5 

112.05 

149.4 

74.7 

1245 

24.5 

66.15 

88.2 

44.1 

735 

42. 

113.4 

151.2 

75.6 

1260 

25. 

67.5 

90. 

45. 

750 

42.5 

114.75 

153. 

76.5 

1275 

382  TVORSTED  REEDS. 

To  ascertain  the  count,  or  fineness  of  worsted  reeds. 

RULE. — Multiply  tlie  number  of  dents  in  an  incli  by  the 
given  number  of  inches  any  reed  is  set  on,  according  to  the  sys- 
tem of  counting,  and  divide  by  20,  •which  is  the  number  of  dents 
in  a  score,  or  beer,  and  the  quotient  will  be  the  count,  or  fine- 
ness of  the  reed,  and  if  the  number  of  dents  in  an  inch  at  the 
reed  be  required,  multiply  the  count  of  the  reed  by  20,  and 
divide  by  the  given  number  of  inches  the  reed  is  set  on,  and  the 
quotient  will  be  the  number  of  dents  in  an  inch,  according  to  the 
fineness  of  the  reed,  and  the  system  of  counting. 

The  system  of  ascertaining  the  count,  or  fineness  of  reeds  for 
lastings,  difi"ers  from  the  others,  but  will  be  found  by  multiplying 
the  number  of  dents  in  an  inch  by  30,  the  product  of  which  will 
be  the  count,  or  fineness  of  the  reed,  and  if  the  number  of  dents 
in  an  inch  be  required,  divide  the  count,  or  fineness  of  the  reed 
by  30,  and  the  quotient  will  be  the  number  of  dents  in  an  inch, 
according  to  the  fineness  of  the  reed. 

EXAMPLES. 

The  count,  or  fineness  of  the  plain  back  reed  containing  19 
dents  in  an  inch  is  required: — 

19,  dents  in  an  inch. 

54,  number  of  inches  the  reed  is 

  set  on. 

76 
95 


Score,  or  beer,  2.0  dents,)102.6 

51.3,  or  51  scores,  or  beers,  and  6 
dents  set  on  54  inches  at  the  reed,  or  nearly  51J  count,  or  fine- 
ness of  the  reed. 

What  number  of  dents  will  there  be  in  an  inch  of  a  51.3  plain 
back  reed  ? 

51.3,  count  of  reed. 

20  dents,  1  score,  or  beer. 

No.  of  inches  reed  set  on,  54)1026.0(19,  number  of  dents  in  an 

54  inch  at  the  reed. 


486 
486 


WORSTED  REEDS. 


383 


WORSTED  EEED  TABLE. 


43. 

43.5 

44. 

44.5 

45. 

45.5 

46. 


46.5125.55 


47. 


47.5128.25 


48. 
48.5 
49. 
49.5 
50. 
50.5 
51. 
51 
52 
52 
53 
53 
54. 


57 
57.0 
58. 
58 
59. 
59. 
60 


o  °  ?, 

Q    «  O 

03  in 


116.1 

117.45 

118.8 

120.15 

121.5 

122.85 

124.2 


126.9 


51 


129.6 
130.95 
132.3 
133.65 
135. 
136.35 
137.7 
9.05 
140.4 
.75 
143.1 
5  144.45 
146.8 
54.5147.15 

55.  148.5 
55.5  149.85 

56.  151.2 
56.5  152.55 

153.9 
155.25 
156.6 
7.95 
159.3 
65 

162. 


515< 


5160. 


154.8 

156.6 

158.4 

160.2 

162. 

163.8 

165.6 

167.4 

169.2 

171. 

172.8 

174.6 

176.4 

178.2 

180. 

181.8 

183.6 

185.4 

187.2 

189. 

190.8 

192.6 

194.4 

196.2 

198. 

199.8 

201.6 

203.4 

205.2 

207. 

208.8 

210.6 

212.4 

214.2 

216. 


77.4 
78.3 
79.2 
80.1 
81. 
81.9 
82.8 
83.7 
84.6 
85.5 
86.4 
87.3 
88.2 
89.1 
90. 
90.9 
91.8 
92.7 
93.6 
94.5 
95.4 
96.3 
97.2 
98.1 
99. 
99.9 
100.8 
101.7 
102.6 
103.5 
104.4 
105.3 
106.2 
107.1 
108. 


1290 
1305 
1320 
1335 
1350 
1365 
1380 
1395 
1410 
1425 
1440 
1455 
1470 
1485 
1500 
1515 
1530 
1545 
1560 
1575 
1590 
1605 
1620 
1635 
1650 
1665 
1680 
1695 
1710 
1725 
1740 
1755 
1770 
1785 
1800 


60.5163 


61. 
61. 
62. 
62. 
63. 
63.5 
04. 
64 
65. 
65.5 
66. 
66 
67. 
67.5 
68. 
68.5 
69. 
69 
70. 


5166. 


5168. 


51 


71. 
71 
72. 
72.5 
73. 
73.5 
74. 
74.5 
75. 
75.5 
76. 
76. 


1 1 . 
77.5 


1^ 


.35 
164.7 

05 
167.4 
.75 
170.1 
171.45 
172.8 
74.15 
175.5 
176.85 
178.2 
5179.55 
180.9 
182.25 
183.6 
184.95 
186.3 

.65 
189. 


5187. 


70.5  190.35 


5193. 


191.7 
.05 
194.4 
195.75 
197.1 
198.45 
199.8 
201.15 
202.5 
203.85 
205.2 
5  206.55 
207.9 
209.25 


a  5 


217.8 

219.6 

221.4 

223.2 

225! 

226.8 

228.6 

230.4 

232.2 

234. 

235.8 

237.6 

239.4 

241.2 

243. 

244.8 

246.6 

248.4 

250.2 

252. 

253.8 

255.6 

257.4 

259.2 

261. 

262.8 

264.6 

266.4 

268.2 

270. 

271.8 

273.6 

275.4 

277.2 

279. 


108.9 

109.8 

110.7 

111.6 

112.5 

113.4 

114.3 

115.2 

116.1 

117. 

117.9 

118.8 

119.7 

120.6 

121.5 

122.4 

123.3 

124.2 

125.1 

126. 

126.9 

127.8 

128.7 

129.6 

130.5 

131.4 

132.3 

133.2 

134.1 

135. 

135.9 

136.8 

137.7 

138.6 

139.5 


384  WORSTED  REEDS. 

The  count,  or  fineness  of  a  wildbore  reed  containing  19  dents 
in  an  inch,  is  required : — 

19  dents  in  an  inch. 

72,  number  of  inches  the  reed  is  set  on. 


38 
133 


Score,  or  beer,  2.0  dnts.)136.8 


68.4  count,  or  fineness  of  the  reed,  i.  e., 
68  scores,  or  beers,  and  8  dents,  or 
1868  dents  set  on  72  inches  at  the  reed. 

What  number  of  dents  will  there  be  in  an  inch  of  68.4  wild- 
bore  reed  ? 

68.4,  count  of  reed. 

20  dents,  1  score,  or  beer. 


No.  of  inches  reed  set  on,  72)1868.0(19,  number  of  dents  in  an 

72  inch  at  the  reed. 


648 
648 


The  count,  or  fineness  of  a  reed,  is  required  from  the  follow- 
ing particulars : — 

Number  of  inches  the  reed  is  set  on,  36. 
Number  of  dents  in  an  inch,  19. 
Number  of  dents  in  a  score,  or  beer,  20. 

19  dents  in  an  inch. 

36,  number  of  inches  the  reed  is  set  on. 


114 
67 


Score,  or  beer,  2.0  dnts.)68.4 


84.2,  count,  or  fineness  of  the  reed,  i.  e., 
34  scores,  or  beers,  and  4  dents,  set  on  36  inches  at  the  reed. 


If  34  scores,  or  beers,  and  4  dents  be  set  on  36  inches  at  the 
reed,  how  many  dents  will  there  be  in  an  inch  ? 


WORSTED  REEDS.  385 

Beers.  Dents. 
34  .  .  4 

20,  number  of  dents  in  a  beer. 


No.  of  inches  reed  set  on,  36)684(19,  number  of  dents  in  an  inch 

36  at  the  reed. 


324 
324 


The  count,  or  fineness  of  lasting  reed  containing  19  dents  in 
an  inch,  is  required  : — 

19  dents  in  an  inch. 
30,  number  of  inches  the  reed  is  set  on. 


570,  or  nearly  5f  count,  or  fineness  of  the  reed. 

reed  contains  570  dents, 
ich? 

No.  of  inches  reed  set  on,  3.0)57.0  dents. 


If  a  lasting  reed  contains  570  dents,  how  many  dents  will 
there  be  in  an  inch? 


19,  number  of  dents  in  an  inch  at 

the  reed. 

How  many  dents  will  there  be  in  an  inch  of  a  50  plain  back 
reed  ? 

50,  count  of  reed. 
20  dents,  1  score,  or  beer. 


No.  of  inches  reed  set  on,  54)1000(18.518,  or  rather  more  than 

54       18|-  dents  in  an  inch  at  the 

  reed. 

460 
432 

280 
270 

100 
54 

460 
432 

28 


386 


MISCELLANEOUS  QUESTIONS. 


N.  B. —  Warps  are  warped  quite  indepmdent  of  the  set  for  which 
they  may  he  used.  The  common  tvay  of  warping  is  hy  portits, 
portives,  porters,  or  heers,  tvhichever  they  may  he  called. 
Some  xoarp  hy  48  ends,  and  lasting  warps  are  generally 
warped  by  48.  Of  course  it  does  not  matter  in  ivhat  numbers 
they  are  tvarped,  if  the  warp  only  contains  the  number  of  ends 
required,  according  to  the  ividth  and  fineness  of  the  reed. 


MISCELLANEOUS  QUESTIONS. 

The  revolutions  a  minute  of  a  shaft  are  required  from  the  fol- 
lowing particulars : — 

Double  strokes  of  steam  engine,  19J  per  minute. 

Wheel  on  crank,  or  fly-shaft,  64  teeth,  working  into  a  wheel  49 
teeth  on  the  first  line  of  shafts. 

Wheel  63  teeth  on  the  first  line  of  shafts,  works  into  a  wheel  36 
teeth  on  foot  of  an  upright  shaft.  Then,  wheel  70  teeth  on 
the  top  of  the  upright  shaft,  works  into  a  wheel  39  teeth  on 
lying  shaft ;  the  speed  of  which  is  required. 

Driving-wheels,  &c. 

19.5  double  strokes,  engine  makes  a  minute. 
64  teeth,  wheel  on  fly,  or  crank  shaft. 


780 
1170 


1248.0 

63  teeth,  wheel  on  first  lying  shaft. 


3744 
7488 

78624 

70  teeth,  wheel  on  top  of  upright  shaft. 


5503680  dividend. 


MISCELLANEOUS  QUESTIONS. 


387 


Driven-wheels. 

49  teeth,  -wheel  on  first  lying  shaft. 

36  teeth,  wheel  on  foot  of  upright  shaft. 


294 
147 


1764 

39  teeth,  wheel  on  lying  shaft,  the  speed 

  of  which  is  required. 

15876 
5292 


68796  divisor. 

68796)5508680(80  revolutions  per  minute,  speed 
550368  of  shaft  required. 


0 

Suppose  a  shaft  be  making  80  revolutions  a  minute,  with  the 
following  driving  and  driven-wheels  on  the  intermediate  shafts  ; 
what  number  of  double  strokes  per  minute  should  the  engine 
make? 

Driving-wheels,  &c. 

80,  revolutions  of  given  shaft  per  minute. 
39  teeth,  wheel  on  do. 


720 
240 


3120 

36  teeth,  wheel  on  foot  of  upright  shaft. 


18720 
9360 


112320 

49  teeth,  wheel  on  the  first  lying  shaft. 


1010880 
449280 


5503680  dividend. 


388 


MISCELLANEOUS  QUESTIONS. 


Drivenw-heels. 

70  teeth,  wheel  on  top  of  upright  shaft. 
63  teeth,  wheel  on  first  lying  shaft. 


210 
420 


4410 

64  teeth,  wheel  on  crank,  or  fly  shaft. 


17640 
26460 


282240  divisor. 

282240)5503680(19.5,  double  strokes  of  steam- 
282240  engine  a  minute. 


2681280 
2540160 


1411200 
1411200 

If  a  drum  42J  inches  diameter,  drives  the  beaters  of  a  blow- 
ing-machine 1344  revolutions  per  minute,  what  must  the  diameter 
of  a  drum  be,  for  the  beaters  to  make  1560  revolutions ;  and  if 
the  present  drum  is  to  be  lagged,  what  thickness  must  the  lags  be  ? 

Revols.     Inches.  Ilevols. 
If  1344  .•  42.25  1560 
1560 


253500 
21125 
4225 


1344)65910.00(49 
5376 


12150 
12096 


.04  inches,  diameter  of  drum  required. 

5400 
6376 


24 


MISCELLANEOUS  QUESTIONS. 


389 


49.04  inches,  diameter  of  drum  required. 
42.25  inches,  diameter  of  given  drum. 

2)6.79  inches,  difference  of  diameters  of  drums. 

3.395,  or  nearly  3.4  inches,  thickness  of  lags 

required. 

If  a  drum  42J  inches  diameter  drives  the  beater  of  a  blowing- 
machine  1844  revolutions  per  minute;  what  number  of  revolutions 
will  the  beater  make  if  driven  from  a  drum  4:9^^^  inches  diameter? 

Inches.  Revols.  Inches. 

If  421  or  42.25  .  •  1344  .  • .  •  49.04,  or  492^ 
49.04 


5376 
120960 
5376 


42.25)65909.76(1560,  revolutions  of  beater  a 
4225  minute,  nearly. 

23659 
21125 


25347 

25350— nearly. 

If  a  pulley  13  inches  diameter  drives  the  main  cylinder  of  a  , 
carding-engine,  at  the  rate  of  126  revolutions  a  minute ;  what 
diameter  must  the  pulley  be,  to  reduce  the  speed  of  the  cylinder 
to  112  revolutions? 

126,  revolutions  given. 
13  inches,  diameter  of  given  pulley. 

378 
126 


1638 


390  MISCELLANEOUS  QUESTIONS. 

Revolutions  req'd,  112)1638(14.625,  or  14|  inches,  diameter  of 
112  pulley  required. 


518 
448 


700 
672 


280 
224 


560 
560 

How  many  grains  will  30  yards  of  3J  hank  roving  weigh  ? 

Hank  roving,  3.25)250.00(76.92  grains,  or  3  dwts.,  5  grains, 
2275  nearly. 


2250 
1950 


3000 
2925 


750 
650 


100 

If  30  yards,  or  |  of  a  lea  weigh  76.92  grains,  what  hank 
roving  will  it  be  ? 

30  yards  of  roving  weigh  76.92)250.00(3.25,  or  3i  hank  roving 

23076 


19240 
15384 


38560 
38460 


MISCELLANEOUS  QUESTIONS. 


391 


The  weight  of  1  pair  of  sets  of  cops  is  required  from  the 
following  particulars: — 

Numher  of  spindles  in  pair  of  wheels,  1016. 

Length  of  stretch  put  up  (breakage  allowed),  61J  inches. 

Number  of  stretches,  900. 

Number  of  yarn  36's. 

1016  X  900  X  61.5  =  56235600.0  dividend. 

840  X  36  X  36  =1088640,  divisor. 

56235600  divided  by  1088640=51  lbs.,  lOJ  oz.,  weight  of 

pair  of  sets. 

How  many  hanks,  leas,  and  yards,  will  there  be  in  a  pair  of 
sets  of  cops,  of  which  the  following  are  the  particulars  ? 

Number  of  spindles  in  wheels,  808. 

Number  of  stretches  on  set,  450. 

Net  length  of  stretch  put  up,  57^-  inches. 

808,  number  of  spindles  in  wheels. 
450,  stretches  on  set. 


40400 
3232 


363600 

67.5,  or  57|  inches,  length  of 

  stretch  put  up. 

1818000 
2545200 
1818000 


{6)20907000.0  number  of  inches  on  pair  of 
  sets. 
6)3484500 

1  lea  is  12.0  yards,)58075.0  yards. 

1  hank  is  7  leas,)4839  leas,  and  70  yards. 


691  hanks,  2  leas,  and  70  yards, 
length  on  pair  of  sets. 


392 


MISCELLANEOUS  QUESTIONS. 


If  there  be  691  hanks,  2  leas,  and  70  yards  on  1  pair  of  sets 
of  number  36's  pincop  weft;  what  weight  will  they  be? 

1  lea  is  12.0  yards, )70.0  yards. 

1  hank  is  7  leas,)2.5888  leas. 


691.36904  hanks,  divided  by  86=19  lbs., 
3J  oz.,  weight  of  691  hanks,  2  leas,  and  70  yards  of  36's  weft. 

If  20  ounces  of  cotton  were  fed  on  30  inches  of  feed-cloth  at 
lap-machine,  and  to  pass  through  all  the  operations  of  working 
without  loss;  what  numbers  of  yarn  would  it  produce,  allowing 
the  following  draughts  and  doublings? 

487.5  grains,  1  oz. 

20  ounces,  weight  of  cotton  fed  on 

  feed-cloth. 

Draught  at  lap-machine,  2)8750.0  grains,  do. 

Dght.  at  card,  engine,  12.0)437.5  grains,  weight  of  80  inches  of 

  lap. 

86.458333  grains,  weight  of  30  in. 
No.  of  ends  put  up  at  1st  drawing,  6  of  carding. 

Dght.  1st  hd.  of  drng.,  6.22)218.750000(35  grains  weight  of  80 

1875  inches,  at  the  1st  head 

  of  drawings. 

3125 
3125 

35  grs.,  wgt.  of  80  in.  of  drng.  1st  head. 
6,  No.  of  ends  put  up  at  2d  hd.  of  drngs. 


210 
189 


MISCELLANEOUS  QUESTIONS. 


393 


33.33  grs.  wgt.  of  30  in.  drag.  2d  hd. 

8,  number  of  ends  put  up  at  3d 

  head  of  drawings. 

Dght.  at  3d  hd.  drngs.,  6.4)266.66(41.666  grs.,  weight  of  30  inches 

256  of  drawing  at  3d  head. 


106 
64 


426 
384 


426 

384 


426 
384 

42 

Dght.  at  slabbing  frame,  5)41.66  grains,  weight  of  30  inches  of 

  drawing,  3d  head. 

8.33  grs.,  wgt.  of  30  in.  of  slabbing. 
2,  no.  of  ends  put  up  at  rov.  frame. 

Draught  at  roving  frame,  7)16.66 

2.38095  grains,  weight  of  30  inches 

of  roving. 

Grains. 

Draught  at  spinning,  11.5)2. 38095(.20704,  decimal  of  a  grain 

230  weight,  of  30  inches 
  of  yarns. 

809 
.805 


26 


450 

460 — nearly. 


394 


MISCELLANEOUS  QUESTIONS. 


.20704  grain,  weight  of  30  inches  of  yarn. 
36,  a  multiplier  for  30  yards. 


124224 
62112 


7.45344  grains,  weight  of  30  yards  of  yarn. 
4 — 4  times  30  yards  =  1  lea. 


29.81376  grains,  weight  of  1  lea  of  yarn. 

The  weight  of  cotton,  according  to  the  foregoing  draughts  and 
doublings,  required  to  produce  1  lea  of  yarn  is  29.81376  grains, 
or  1  dwt.,  5.81376  grains. 

Weight  of  1  lea,  29.81376  grns.)1000. 00000(33.54  hanks  in  1  lb. 

8944128 


10558720 
8944128 


16145920 
14906880 


33.54  hanks  =  1  lb. 
8.385  hanks  =  4  ounces. 


41.925  hanks  =  20  ounces. 
7  leas  =  1  hank. 


293.475 

29.8137  grains  =1  lea. 


2054325 
880425 
293475 
2347800 
2641275 
586950 


8749.5756075  grains  weight,  or  20  ounces 
fed  on  80  inches  of  feed  cloth  at  lap  machine. 


12390400 
11^25504 


464896 


I 

■ 


MISCELLANEOUS  QUESTIONS. 


395 


If  20  ounces  of  cotton  fed  on  80  inches  of  feed  cloth  at  lap 
machine  produces  number  36's  twist,  or  weft,  according  to  the 
following  draughts  and  doublings  ;  what  will  the  loss  sustained 
in  working  be? 

Draught  at  the  lap  machine,  2. 
Draught  at  the  carding  engine,  120. 
Draught  at  the  1st  head  of  drawings,  6.25. 
Draught  at  the  2d  head  of  drawings,  6.3.- 
Draught  at  the  3d  head  of  drawings,  6.4. 
Draught  at  the  slabbing  frame,  5. 
Draught  at  the  roving  frame,  7. 
Draught  at  the  spinning,  11.5. 
Multiplier  for  30  inches,  6.944. 

Doublings  at  the  1st  head  of  drawings,  6. 
Doublings  at  the  2d  head  of  drawings,  6. 
Doublings  at  the  3d  head  of  drawings,  8. 
Doublings  at  the  roving  frame,  2. 
Numbers  of  yarn  produced,  36's. 

Draughts. 

2,  lap  machine. 
120,  carding  engine. 

240 

6.25,  first  head  of  drawings. 

1200 
480 
1440 


1500.00 
6.3,  second  head  of  drawings. 

4500 
9000 


9450.0 

6.4,  third  head  of  drawings. 


37800 
56700 


396 


MISCELLANEOUS  QUESTIONS. 


60480.0 

5,  slabbing  frame. 

302400 

7,  roving  frame. 

2116800 

11.5  mules. 


10584000 
23284800 


24343200.0 
Mult.forSOin.,  asper  table,6.944 


97372800 
97372800 
219088800 
146059200 


169039180.800  dividend. 


Doublings. 
6x6x8x2x36  =  20736  divisor. 

169039180.8  divided  by  20736  =8152  grains,  or  18  oz.,  11  dwt., 
13  grains,  weight  of  yarn  produced  from  20  oz.  of  cotton. 

oz.  dwts.  grs. 

Weight  of  cotton  fed  on  feed  cloth  at  lap  machine,  20  . .  0  . .  0 
Weight  of  yarn  produced,     .       .       .       .    18  . .  11  . .  13 

Loss  sustained  in  working,    .       .       .       .      1 . .   6  . .  16.5 

Suppose  there  be  a  48  teeth  wheel  working  into  a  36  teeth 
wheel,  and  finding  them  of  a  finer  pitch  than  they  should  be ; 
what  wheels  will  work  in  the  same  place  to  pi'oduce  the  same 
speed  with  the  same  diameters  of  wheels? 

RULE. — Reduce  the  wheels  to  their  lowest  terms,  by  dividing 
them  by  any  number  that  will  divide  the  number  of  teeth  in 
the  wheels  without  a  remainder ;  then  multiply  the  lowest  terms 
of  the  wheels  by  any  one  number  that  will  produce  the  number 
of  teeth  required. 


MISCELLANEOUS  QUESTIONS. 

Tims, 


397 


12)48 

Lowest  term,  4 

Lowest  term,  4 
2 


12)86 

3  lowest  term. 

3  lowest  number. 
2 


Wheel,  8  teeth,  and  wheel  6  teeth. 


Lowest  term,  4 
3 


3  lowest  term. 
3 


Wheel,  12  teeth,  and  wheel  9  teeth. 


Lowest  term,  4 
4 


3  lowest  term. 
4 


Wheel,  16  teeth,  and  wheel,  12  teeth. 


Lowest  term,  4 


3  lowest  term. 
5 


Wheel,  20  teeth,  and  wheel,  15  teeth. 


Lowest  term,  4 
6 


3  lowest  term. 
6 


Wheel,  24  teeth,  and  wheel,  18  teeth. 


Lowest  term,  4 
9 


3  lowest  term. 
9 


Wheel,  36  teeth,  and  wheel,  27  teeth. 

N.B. — The  same  system  will  answer,  either  for  increasing  or 
decreasing  the  number  of  teeth  in  tvheels. 

Any  of  the  above  wheels  working  together  will  produce  the 
same  speed. 


398 


JUDKINS'  AMERICAN  HEALDS. 


JUDKINS'  AMERICAN  HEALDS,  OR  PATENT 
HEDDLES. 

PLATE  I. 

The  machine  shown  in  the  drawing  is  so  constructed  as  to 
double  and  twist  the  yarn  from  single  of  itself,  and  at  the  same 
time,  at  certain  points,  is  converted  into  a  braiding  or  platting 
machine,  by  which  the  eye  or  loop  of  the  heddle  is  formed,  with- 
out knots  of  any  description. 

The  advantages  of  this  machine  are  many.  A  set  of  healds  is 
produced  by  it  at  a  much  less  cost  than  by  any  other  method,  and 
without  a  single  knot  at  any  point,  the  whole  being  one  continu- 
ous twine  or  cord. 

By  the  drawing  is  also  shown  a  set  of  healds  made  by  this 
machine,  with  the  eye  or  loop  as  described,  which  is  coated,  lined, 
or  covered  with  a  metallic  substance,  suitable  for  the  purpose. 

One  set  of  patent  healds  will  last  fifteen  of  any  other  kind, 
and  a  greater  number  of  yards  of  cloth,  heavier  and  more  perfect, 
can  be  produced  through  it,  in  a  given  time,  in  consequence  of 
less  friction  upon  the  warp. 


mason's  self-acting  mule. 


399 


MASON'S  SELF-ACTING  MULE. 

PLATES  II.  III.  IV.  V. 

Of  this  machine  we  give  the  inventor's  specification  complete : 
The  schedule  referred  to  in  the  letters  patent  and  making  part 
of  the  same. 

To  all  to  whom  these  jyresents  shall  come — Be  it  known,  that 
I,  William  Mason,  of  Taunton,  in  the  County  of  Bristol  and 
State  of  Massachusetts,  have  invented  a  new  and  useful  self-acting 
mule  for  spinning  cotton  and  other  fibrous  substances,  and  that 
the  following  is  a  full,  clear  and  exact  description  of  the  principle 
or  character  which  distinguishes  it  from  all  other  things  before 
known,  and  of  the  manner  of  making,  constructing  and  using  the 
same,  reference  being  had  to  the  accompanying  drawings,  making 
part  of  this  specification,  in  which  Fig.  1  is  an  elevation  of  the 
head  of  the  mule  next  the  carriage — Fig.  2  an  elevation  of  the 
opposite  side — Fig.  3  a  plan — Fig.  4  a  back  elevation — Fig. 
5  a  longitudinal  vertical  section  taken  at  the  line  (XX)  of  Fig. 
3,  looking  in  the  direction  of  the  arrow — Fig.  6  a  front  eleva- 
tion— Fig.  7  a  section  of,  and  through  the  friction  clutch — Fig. 
8  separate  view  of  the  scroll  or  volute  cam — and  Fig.  9  a  ver- 
tical cross  section  of  the  head  taken  just  in  front  of  the  shipper 
lever.    The  same  letters  indicate  like  parts  in  all  the  figures. 

The  motions  of  the  mule  may  be  divided  into  three  series,  which 
are  subdivided  in  the  action  of  the  apparatus.  The  first  series 
consists  of  the  drawing  out  of  the  carriage,  the  revolving  of  the 
draw-rollers  and  the  whirling  of  the  spindles,  by  means  of  which 
series  of  motions  the  rovings  are  drawn  out  and  the  threads  spun 
and  twirled.  The  second  series  consists  of  backing  ofi",  as  it  is 
termed,  that  is,  turning  the  spindles  the  reverse  direction,  to  un- 
coil the  threads  from  the  points  of  the  spindles  to  the  cops  and 
turning  down  or  depressing  the  front  filler,  at  the  same  time  to 
place  all  the  parts  in  a  proper  con-dition  for  the  third  series  of 
motions,  Avhich  consists  of  putting  or  running  in  the  carriage, 
winding  on  the  yarn  or  threads  by  giving  a  vai-ying  motion  to  the 
spindles  corresponding  to  the  form  and  size  of  the  cops,  and  ope- 
rating the  faller  to  give  the  proper  shape  to  the  cops. 


400 


mason's  self-acting  mule. 


The  first  series  of  motions  is  regular.  The  carriage  is  drawn 
out  by  a  regular  motion,  effected  by  a  train  of  wheels  from  the 
driving  pulley  to  a  line  shaft,  which  carries  endless  chains  con- 
nected with  the  carriage  at  different  parts  of  its  length  to  insure 
steadiness  of  motion.  During  this  the  draw-rollers  are  rotated, 
to  give  out  the  staple  as  it  is  spun  by  another  train  of  wheels 
deriving  motion  from  the  same  source  as  the  preceding,  and  in  a 
manner  substantially  similar  to  other  mules.  And  at  the  same 
time  the  spindles  are  whirled  or  rotated  by  a  band  receiving  mo- 
tion from  a  pulley  on  the  shaft  of  the  driving  pulley  as  in  other 
mules.  This  completes  the  first  series  of  motions,  in  which  I 
claim  nothing  new. 

At  the  end  of  the  first  series  of  motions,  the  threads  that  have 
been  spun  are  coiled  on  the  spindles  from  the  cops  to  their  points 
— it  is  therefore  necessary  to  uncoil  them  (called  "backing  off") 
preparatory  to  winding  on,  and  at  the  same  time  to  depress  the 
front  faller  to  place  it  in  a  proper  position  for  winding  on.  The 
second  series  of  motions  en'ects  these  purposes,  and  the  various 
parts  of  the  mechanism  are  put  in  a  proper  condition  to  effect 
this  by  the  momentum  of  the  moving  parts  at  the  end  of  the  fix'st 
series  of  motions.  This  constitutes  the  first  part  of  my  invention. 
As  the  carriage  approaches  the  end  of  the  out  motion,  the  driving 
belt  is  shifted  from  the  first  driving  pulley  to  a  loose  pulley  by 
the  side  of  it,  to  permit  the  momentum  of  the  moving  parts  to 
complete  the  movements,  and  so  soon  as  these  are  accomplished 
a  balance  weight  is  carried  beyond  the  vertical  line  and  falls  over, 
which  shifts  the  belt  from  the  loose  pulley  to  a  second  fast  pulley 
on  the  same  shaft  with  the  others,  at  the  same  time  the  trains  of 
wheels  that  operate  the  carriage  and  the  draw-rollers  are  liberated 
by  the  shifting  of  a  clutch,  and  at  the  same  time  a  friction  clutch 
is  brought  into  action,  thereby  connecting  the  band  that  drives 
the  spindles  with  a  sliding  rack  (called  the  "top-sliding  rack") 
which,  in  consequence  of  this  connection,  is  carried  by  the  mo- 
mentum of  the  spindles  sufficiently  far  in  one  direction  to  give 
by  its  return  the  required  motion  to  the  spindles  in  the  reverse 
direction  to  uncoil  the  threads  from  the  upper  parts  of  the 
spindles.  Whilst  the  rack  is  thus  moved,  the  second  fast  pulley 
sets  in  motion,  by  a  train  of  wheels,  a  crank  pin  that  works  in  a 
slot  in  a  connecting  rod,  and  this  crank  pin  when  set  in  motion 
is  a  little  below  a  line  passing  through  the  connecting  rod  and  the 
axis  of  motion,  so  that  the  crank  pin  moves  a  short  distance  before 
it  begins  to  move  the  connecting  rod — this  period  of  time  is  suffi- 
cient to  permit  the  momentum  of  the  spindles  (as  above  stated) 


mason's  self-acting  mule. 


401 


to  draw  the  sliding  rack  to  the  distance  required  to  be  in  a  con- 
dition, by  its  return  movement,  to  give  the  "backing-off"  m-otioii? 
to  the  spindles.  The  ci'ank  pin  then  in  making  a  semi-revolution 
carries  the  connecting  rod  with  it,  and  this  being  in  connection 
with  the  lever  of  a  rock  shaft,  provided  with  a  toothed  pulley, 
around  which  passes  a  chain  attached  to  the  end  of  the  sliding 
rack,  draws  it  (the  rack)  for  a  short  distance  in  a  reverse  direction, 
and  thus  causes  it  to  give  the  backing-ofF  motion  to  the  spindles, 
to  uncoil  the  threads,  at  the  same  time  depressing  the  front  faller 
to  bring  the  threads  in  a  proper  position  for  winding  on,  this  latter 
being  effected  by  having  one  end  of  the  shaper  or  coping  rail 
jointed  to  a  lever  on  the  rock  shaft  above-mentioned.  The  chain 
attached  to  the  rack  and  which  communicates  motion  to  it,  is  kept 
tight  by  being  passed  over  a  pulley  and  having  a  weight  suspended 
to  it. 

When  the  top-sliding  rack  is  carried  forward  by  the  momentum 
of  the  spindles  at  the  end  of  the  first  series  of  motions,  it  is  gra- 
dually arrested,  and  with  it  the  spindles,  by  means  of  a  spring 
brake  of  a  peculiar  construction,  viz. : — On  the  rock  shaft  there 
is  a  bent  lever,  to  one  end  of  which  is  connected  a  helical  spring 
also  attached  to  an  arm  jointed  to  the  other  end  of  the  bent  lever : 
and  by  the  side  of  and  attached  to,  the  toothed  wheel,  around 
which  passes  the  chain  on  the  end  of  the  sliding  rack,  and  which 
turns  freely  on  the  rock  shaft,  there  is  a  ratchet  wheel  and  by 
the  side  of  it  a  cam  plate  provided  with  a  hand  or  catch,  by 
means  of  which  the  ratchet  and  toothed  wheels  are  carried  ai'ound, 
when  the  cam  plate  is  carried  around  by  the  action  of  the  spring 
brake  on  the  cam  form  of  its  periphery.  And  when  this  has 
been  carried  far  enough  arOund,  the  catch  is  liberated  to  permit 
the  return  of  the  parts  by  means  of  an  arm  or  lever  jointed  to 
one  end  of  the  bent  lever  which  is  made  to  lift  the  catch  from 
the  teeth  of  the  ratchet  wheel.  As  the  cops  increase  in  diame- 
ter, it  is  evident  that  the  backing-off  motion  must  be  diminished, 
and  this  is  effected  by  making  the  connecting  rod  above-mentioned 
in  two  parts,  the  first  connected  by  one  end  (as  above  stated)  with 
the  crank  pin  which  actuates  it  and  which  works  in  a  slot  to  give 
motion  to  the  rod  in  one  direction  only  (the  crank  being  then  at 
liberty  to  turn  without  imparting  any  motion  longitudinally  to  the 
rod),  the  other  end  being  jointed  to  a  curved  arm  that  vibrates 
on  a  stud  pin,  and  the  other  part  of  the  connecting  rod  is  jointed 
to  the  arm  of  the  rock  shaft  and  to  a  slide  that  works  in  a  curved 
groove  ia  the  vibrating  arm,  so  that  as  this  slide  is  moved  from 
or  towards  the  axis  of  motion  of  the  arm,  the  rock  shaft  will  be 


402 


mason's  self-acting  mule. 


vibrated  more  or  less  and  this  slide  is  moved  in  or  out  by  being 
in  connection  with  the  mechanism  that  operates  the  motions  of 
the  coping  rail,  and  which  will  therefore  be  described  under  the 
third  series.  At  the  end  of  the  backing-off  motion,  the  vibrating 
arm  of  the  connecting  rod  is  hooked  and  held  by  a  catch  until 
the  carriage  is  run  up,  and  then  liberated  to  permit  the  parts  to 
resume  their  appropriate  positions  preparatory  to  a  repetition  of 
the  operation. 

At  the  end  of  the  second  series  of  motions  the  third  series  of 
motions  commences,  and  these  constitute  the  second  part  of  my 
invention.  The  carriage  is  run  in  by  a  crank  motion,  which  has 
the  effect  to  gradually  start  it  from  a  state  of  rest,  and  accele- 
rate its  motion  to  the  middle  of  its  course,  and  then  gradually 
diminish  its  motion  until  it  is  brought  to  a  state  of  rest — thus 
avoiding  all  tendency  to  break  the  threads  consequent  upon  all 
sudden  motions.  This  is  effected  in  the  following  manner,  viz.  : 
When  tlie  shipping  lever  is  operated  at  the  end  of  the  first  series 
of  motion,  a  clutch  on  a  shaft  carried  by  the  second  fast  pulley 
is  shifted,  and  on  this  clutch  has  but  one  tooth,  the  shaft  is  there- 
by permitted  to  make  part  of  a  revolution,  during  which  the 
second  series  of  operations  takes  place  before  it  (the  clutch)  be- 
gins to  act,  and  then  it  communicates  motion  to  a  large  cog- 
wheel provided  with  a  crank  pin,  that  actuates  a  connecting  rod 
jointed  to  a  rack  (below  the  top-sliding  rack  above  described), 
the  teeth  of  which  take  into  the  teeth  of  a  pinion  on  the  shaft 
of  one  of  the  train  of  wheels  that  communicate  motion  to  the 
carriage,  thereby  imparting  the  desired  movement.  The  wind- 
ing on  of  the  yarn  during  the  running  in  of  the  carriage  is  ef- 
fected by  the  top  sliding  rack,  which  for  the  purpose  is  carried 
by  the  rack  just  described,  by  means  of  such  connections  as  ad- 
mit of  modifying  the  motions  of  the  top-sliding  rack  which  drives 
the  spindles  in  winding  on.  Motion  is  communicated  from  the 
bottom  to  the  top  rack  in  the  following  manner  : — On  the  end 
of  the  lower  rack  and  by  the  side  of  it,  there  is  a  stud  pin 
on  which  turns  a  scroll  cam,  and  to  that  part  of  its  periphery 
which  is  nearest  the  axis  is  attached  one  end  of  a  chain,  which 
passes  from  thence  around  a  roller  that  turns  on  a  stud  pin  at 
the  side  of  the  lower  rack,  and  is  then  carried  back  and  attached 
by  a  short  arm  to  the  top-sliding  rack,  so  that  when  the  lower 
rack  slides  the  top  rack  will  move  with  it,  provided  the  scroll 
can  remain  immovable  on  its  axis,  but  as  the  motion  of  the  top 
rack  during  each  operation  must  have  a  motion  accelera,tcd  rela- 
tively to  that  of  the  lower  rack,  to  increase  the  rotation  of  the 


a 


mason's  self-acting  mule. 


403 


spindles,  as  the  threads  are  wound  on  a  gradually  diminishing 
diameter  of  the  conical  form  of  the  cops — this  is  eifected  by 
causing  the  scroll  cam  to  turn  on  its  axis  during  the  motion  of 
the  rack,  by  having  a  wheel  attached  to  and  turning  with  it,  to 
the  periphery  of  which  is  attached  one  end  of  a  chain,  that 
passes  around  it,  and  is  attached  by  the  other  end  to  another 
part  of  the  machine,  so  that  if  this  part  of  the  attachment  re- 
mains fixed,  a  regular  accelerated  motion  will  be  given  to  the 
top  rack,  relatively  to  the  motion  of  the  lower  rack,  and  neces- 
sarily the  spindles  will  have  their  rotation  accelerated  relatively 
to  the  motion  of  the  carriage.  These  relative  motions  of  the 
two  racks,  as  described,  are  such  as  are  required  after  the  base 
of  the  cops  has  been  formed,  for  then  the  threads  are  wound 
regularly  on  a  cone  :  but  in  forming  the  base  of  the  cops  the 
first  winding  is  on  the  naked  spindles,  at  which  time  the  motion 
of  the  spindles  should  correspond  with  that  of  the  carriage,  and 
from  the  commencement  until  the  base  is  formed,  the  accelerated 
motion  should  be  gradually  brought  into  play,  to  give  the  conical 
form  to  the  cops.  This  is  effected  by  having  the  chain  that 
winds  on  the  wheel  that  turns  with  the  scroll  cam,  attached  to  a 
slide  that  works  on  a  screw  in  a  vibrating  arm,  the  outer  end  of 
which  is  jointed  to  another  arm  of  equal  length,  that  turns  on 
the  end  of  the  stud,  on  Avhich  the  scroll  cam  and  wheel  turn,  so 
that  when  the  slide  is  at  the  lower  end  of  the  arm,  the  two  arms 
being  of  equal  length,  the  motion  of  the  wheel  with  the  rack  will 
not  cause  it  to  wind  up  the  chain,  but,  as  the  slide  is  drawn  up 
towards  the  axis  of  vibration  of  the  arm,  one  end  of  the  chain 
Avill  necessarily  move  through  a  less  space  than  the  other,  and 
thus  cause  the  wheel,  with  the  scroll  cam  attached  thereto,  to 
turn  on  its  axis,  and  thus  to  vai-y  the  motion  of  the  top  rack, 
and  thereby  adapt  the  motion  of  the  spindles  to  the  varying 
diameter  of  the  base  of  the  cops.  The  screw  in  the  vibrating 
arm  that  carries  the  slide,  is  in  connection  by  means  of  appro- 
priate cog-wheels  with  a  horizontal  ratchet  wheel,  which  is  free  to 
move  when  the  arm  vibrates  in  one  direction,  but  held  by  the 
hand  or  catch  when  the  arm  vibrates  in  the  reverse  direction, 
for  the  purpose  of  turning  the  screw  to  move  the  slide :  and  this 
hand  or  catch  is  governed  by  an  apparatus  called  a  butterfly, 
which  is  acted  on  by  an  arm  from  the  counter-faller,  when  the 
tension  of  the  thread  is  too  great,  and  thus  throws  the  hand  into 
the  teeth  of  the  wheel,  that  the  vibration  of  the  arm  shall  ope- 
rate the  slide — the  hand  or  catch  being  disengaged  at  each  run- 
ning out  of  the  carriage.    The  last  of  the  third  series  of  mo- 


404 


mason's  self-acting  mule. 


tions  is  the  operation  of  the  coping  rail  for  operating  the  faller, 
which  being  essentially  similar  to  others,  needs  no  special  notice 
here. 

At  the  end  of  the  running  in  motion  of  the  carriage,  a  pin  on 
an  arm  projecting  from  the  shaft  of  the  crank  that  operates,  the 
under  rack  liberates  the  catch  that  holds  the  connecting-rod,  by 
which  the  backing- off  motion  is  effected,  and  so  soon  as  it  is 
liberated,  the  weight  of  the  machinery  attached  draws  it  back 
— and  to  prevent  any  sudden  jar  by  this  operation,  the  crank 
pin  which  operates  the  connecting  rod  in  one  direction,  is  so 
governed  in  its  revolutions  as  to  be  neaidy  a  semi-revolution  from 
its  point  of  departure,  at  the  commencement  of  the  backing-off 
operation,  so  that  the  force  required  for  carrying  it  back  to  this 
position  is  sufficient  to  ease  off  the  motion  of  the  returning  parts. 
This  crank  pin  is  held  in  the  position  just  indicated  by  a  brake 
within  the  second  fast  pulley,  and  this  brake  is  connected  by  a 
joint  link  and  lever  with  the  arm  of  the  connecting-rod  of  the 
backing  off  apparatus,  which,  when  drawn  back,  forces  the  brake 
in  contact'  with  the  pulley,  and  arrests  the  train  of  wheels  and 
this  crank  pin  in  their  appropriate  place. 

When  finishing  the  caps  it  is  important  to  wind  the  threads  on 
tight  at  the  point,  particularly  as  the  upper  ends  of  the  spindles 
are  tapering.  This  is  effected  by  forming  the  connection  between 
the  chain  and  the  end  of  the  top  sliding  rack  by  means  of  a  vibrat- 
ing frame,  from  Avhich  projects  another  arm  that  has  a  chain 
jointed  to  it,  extending  to  and  winding  on  an  arbor,  which  arbor 
has  a  ratchet-wheel  on  it,  which  is  carried  a  part  of  a  revolution 
at  each  operation  of  the  mule  by  a  hand  on  the  arm  of  the  con- 
necting rod  of  the  backing-off  motion ;  and  this  auxiliary  chain  is 
of  such  length  that  it  continues  to  be  wound  upon  the  arbor  with- 
out affecting  the  operations  of  any  part  of  the  machinery  until 
the  caps  are  nearly  completed,  and  then  it  becomes  so  short  as  to 
be  brought  in  contact  with  a  permanent  arm  towards  the  end  of 
the  winding-on  operation,  and  when  thus  brought  in  contact  with 
this  arm  it  suddenly  shortens  the  chain  that  forms  the  connection 
between  the  two  racks,  and  necessarily  increases  the  rotation  of 
the  spindles,  which,  as  a  necessary  consequence,  draws  the  threads 
tighter  on  the  spindles. 

In  the  accompanying  drawings  (A^)  represents  a  frame  pro- 
perly adapted  to  the  operative  parts  of  Avhat  constitutes  the  head 
of  the  mule,  the  carriage  not  being  represented,  as  it  is  in  every 
particular  similar  to  other  mules.  (A  A'  A")  are  three  pulleys 
of  equal  diameter  and  placed  side  by  side  on  the  main  shaft  (B). 


mason's  SELF-ACima  MULE. 


405 


The  one  (A)  is  the  first  fast  pulley  attached  to,  and  turning  with 
the  shaft  (B).  (A^)  is  the  second  fast  pulley,  carrying  a  pinion 
(D),  and  turning  freely  on  the  shaft  (B),  and  (A")  is  a  loose  pulley 
placed  between  the  other  two  and  turning  freely  on  the  shaft. 
A  driving  belt  from  some  first  mover  passes  over  these  pulleys  and 
is  guided  to  either  of  them  by  a  shipper  lever  (C)  that  vibrates  on 
a  steel  pin  (W),  and  connected  with  a  weighted  balance  lever  (C^), 
by  which  it  is  operated  when  the  belt  is  to  be  shipped  from  one 
to  another  of  these  pulleys.  [At  the  commencement  of  the  first 
series  of  operations,  the  belt  runs  on  the  first  fast  pulley  (A'),  to 
give  the  first  series  of  motions.  The  pinion  (J)  on  the  shaft  (B) 
communicates  a  positive  and  regular  motion  to  the  shaft  (G), 
(which  is  in  connection  with  the  draw  rollers  in  the  usual  manner), 
by  means  of  the  first  train  of  wheels  (K,  L,  J),  and  from  the 
shaft  (G)  by  the  second  train  of  wheels  (N,  0,  P,  R,  S,  X),  to 
the  line  shaft  (Y)  that  drives  the  carriage  by  means  of  endless 
chains  (Z)  connected  with  the  carriage  by  one  of  the  links  (Z^). 

There  is  but  one  of  these  chains  represented  in  the  drawings, 
and  the  shaft  is  shown  as  broken  off",  as  the  connections  with  the 
carriage  present  nothing  new,  and  therefore  need  not  be  repre- 
sented. And  at  the  same  time  the  spindles  are  rotated  or  whirled 
by  the  usual  band  (T'),  diiven  by  the  pulley  (0'),  on  the  same 
pulley  shaft  (B).  This  completes  the  first  series  of  motions, 
viz :  drawing  out  the  carriage,  rotating  the  draw  rollers,  and 
whirling  the  spindles,  to  draw  out,  spin  and  twist  the  threads. 

Towards  the  end  of  the  running  out  motion  of  the  carriage, 
the  belt  is  shipped  from  the  first  fast  pulley  (A)  to  the  loose  pulley 
(A")  which  removes  the  driving  power  from  these  motions.  This 
shifting  of  the  belt  is  effected  in  the  following  manner,  viz :  the 
weighted  balance  lever  (C^)  is  jointed  to  the  shipper  lever  at 
(2),  and  above  the  stud  pin  (3),  on  which  it  vibrates,  its  upper 
end  being  weighted  to  enable  it  to  fall  over  by  gravity,  after  the 
weight  has  been  carried  a  little  beyond  the  vertical  line.  The 
lower  end  of  this  balance  lever  is  T  formed,  and  one  of  its  short 
arms  is  jointed  by  a  link  (4),  with  a  short  lever  (5)  that  turns  on 
a  stud  pin  (6),  and  this  lever  is  also  connected  by  a  link  [d)  with 
another  lever  (A)  that  turns  on  a  stud  pin  (c),  and  this  last  lever 
is  depressed  when  the  belt  is  to  be  slipped  by  means  of  a  pin  [a) 
in  a  vibrating  arm  (L')  on  the  shaft  (K^)  of  the  wheel  that  carries 
the  connecting  rod  by  which  the  carriage  is  run  in.  The  balance 
lever  is  by  this  means  carried  a  little  beyond  the  vertical  line, 
and  then  carried  entirely  over  by  the  weight  of  the  lever  (C^). 
On  this  same  shaft  (K'),  and  on  the  opposite  side  of  the  frame 


406 


mason's  self-acting  mule. 


there  is  another  arm  (M')  provided  with  a  pin  {g\  which  at  the 
same  time  depresses  another  lever  (N^),  converted  by  means  of  a 
jointed  rod  (/<)  with  an  elbow  lever  (7)  that  operates  a  clutch  (M) 
on  the  shaft  (G)  by  means  of  which  the  cog-wheel  (I)  is  clutched 
to  its  shaft,  or  unclutched,  so  that  when  the  driving  belt  is  re- 
moved from  the  fast  pulley  (A)  to  disconnect  the  parts  that  give 
the  first  series  of  motions  to  the  wheel  (I)  is  unclutched,  which  libe- 
rates the  draw  rollers,  and  the  second  train  of  wheels  that  com- 
municate motion  to  the  carriage  from  the  parts  that  drive  the 
spindles,  so  that  they  (the  spindles)  are  free  to  continue  to  move 
by  their  momentum  independent  of  the  draw  rollers  and  carriage. 
The  clutch  (M)  is  held  open  until  the  belt  is  again  carried  to  the 
first  fast  pulley  at  the  end  of  the  third  series  of  motions  by  a 
pin  (y)  in  one  arm  of  the  balance  lever  (C^)  which  bears  against 
one  side  of  the  arm  of  the  clutch  lever  (7),  for  the  lever  (N')  that 
operates  the  clutch  lever  is  provided  with  a  helical  spring  [i) 
attached  to  it  and  the  frame,  for  the  purpose  of  forcing  the  clutch 
in  the  moment  that  the  pin  (  /)  of  the  balance  lever  (C^)  liberates 
the  clutch  lever  (7).  The  parts  being  thus  situated,  and  the 
driving  belt  in  the  loose  pulley,  the  momentum  of  the  spindles 
will  cause  them  to  continue  to  turn  for  some  time,  and  thus  com- 
mences the  second  sex'ies  of  motions. 

The  band  (T')  that  carries  the  spindles,  and  which,  as  stated 
above,  passes  around  and  is  carried  by  the  pulley  (0')  on  the  main 
shaft  (B),  passes  around  a  guide  pulley  (R')  at  one  end  of  the 
frame,  and  another  (S')  at  the  other  end,  and  also  around  another 
pulley  (P^)  that  runs  freely  on  a  shaft  (Q'),  except  when  clutched 
to  it,  which  is  done  at  the  time  the  driving  belt  is  slipped  from 
the  first  fast  pulley  (A).  This  pulley  (P'),  called  the  "friction 
clutch  pulley,"  is  a  hollow  cone  lined  with  leather,  into  which  is 
received  a  conical  friction  clutch  (P")  attached  to  the  end  of  the 
shaft  (Q'),  which  slides  endwise  in  its  bearings,  and  in  the  friction 
pulley,  which  is  prevented  from  sliding  endwise  with  the  shaft  by 
a  collar  (8);  so  that,  when  this  shaft  (Q')  is  moved  in  one  direc- 
tion, the  pulley  (P')  is  clutched  to  it  by  the  friction  of  the  conical 
surfaces,  and  when  moved  in  the  reverse  direction,  it  is  unclutched, 
and  turns  freely  on  the  shaft.  This  clutching  and  unclutching 
is  effected  by  an  arm  (Z^Fig.  5),  on  the  spindle  (XT')  of  the  shipper 
lever  (C),  which  embraces  a  collar  on  the  shaft  (Q'),  so  that  when 
the  shipper  (C)  shifts  the  belt  from  the  first  fast  pulley  (A),  it  at 
the  same  time  gives  the  requisite  movement  to  clutch  the  friction 
clutch  that  connects  the  spindles  with  the  shaft  (Q'),  which  will 
be  carried  by  their  momentum,  and  as  this  shaft  is  connected  by 


mason's  self-acting  mule. 


407 


the  train  of  wheels  (X',  Y\  7}  and  C"),  with  a  horizontally  sliding 
rack  (W'),  it  (the  rack)  will  be  carried  for  a  short  distance  in  the 
direction  of  the  arrow  thereon.  See  Fig.  5.  When  the  shipper 
transfers  the  belt  from  the  first  fast  to  the  loose  pulley,  a  clutch 
(D^)  Fig.  9,  on  the  shaft  (Di)  is  shifted  by  the  forked  lever  (/), 
which  turns  on  the  stud  pin  (10),  and  is  operated  by  a  spur  (11) 
on  the  balance  lever  (C^),  which  bears  on  the  end  of  a  volute 
spring  (12)  attached  to  the  lever  (/),  the  tension  of  which  forces 
the  sliding  part  of  the  clutch  against  the  permanent  part,  which, 
having  but  one  cog,  causes  it  to  clutch,  when  by  the  rotation  of 
the  shaft  the  parts  coincide.  The  sliding  part  of  the  clutch  is 
feathered  to  the  shaft  (D'),  which  is  carried  by  a  train  of  wheels 
(C^  B^),  and  pinion  (D),  on  the  second  fast  pulley  (A'),  driven  by 
the  driving  belt,  when  it  is  shifted  by  the  shipper,  which  carries 
it  from  the  first  fast  pulley  (A)  to  the  loose  pulley  (A''),  and  then 
to  this,  the  time  required  for  this  transfer  of  the  belt  by  the  mo- 
tion of  the  shipper  being  sufficient  for  the  preparatory  movements. 

So  far,  it  has  been  shown,  that  the  second  fast  pulley  carries 
the  shaft  (D')  of  the  clutch  (D^)  a  part  of  a  revolution,  before 
clutching  the  pinion  (E^)  which  gears  into  the  wheel  (F^)  that 
runs  the  carriage  in  (as  will  be  hereinafter  described),  this  period 
of  time  being  required  to  enable  the  momentum  of  the  spindles 
to  run  back  the  rack  (W*)  preparatory  to  the  backing-o£F  motion. 

As  the  rack  (W')  is  carried  by  the  momentum  of  the  spindles 
in  the  direction  of  the  arrow,  preparatory  to  the  backing- off  mo- 
tion, it  is  necessary  gradually  to  arrest  this  motion,  which  is 
effected  by  a  friction-spring  brake,  constructed  and  connected 
with  the  rack  in  the  following  manner.  To  the  end  of  the  rack 
is  attached  a  chain  (w),  which  passes  over  a  pulley  (o),  and  then 
around  a  spur-wheel  (p),  attached  to  a  ratchet-wheel  (ff),  and 
with  it  turning  freely  on  a  rock-shaft  («),  and  then  it  passes  over 
another  loose  pulley  (D^),  and  to  the  end  of  it  is  suspended  a  ten- 
sion weight  (E^),  which  takes  up  the  slack  of  the  chain.  On  the 
said  rock-shaft  (*i),  and  by  the  side  of  the  ratchet-wheel,  there  is 
a  cam  plate  (^),  that  also  turns  freely  on  the  shaft,  and  which  is 
carried  in  one  direction  by  the  ratchet-wheel,  when  the  catch  or 
hand  (w),  which  is  jointed  to  the  cam-plate,  takes  into  the  teeth 
of  the  ratchet,  the  two  turning  independently  of  each  other  in 
the  reverse  direction,  or  in  the  same  direction,  when  the  catch  or 
hand  is  lifted  out  of  the  teeth.  When  the  rack  is  drawn  by  the 
momentum  of  the  spindles  in  the  direction  of  the  arrow,  the 
chain  {m)  attached  thereto  turns  the  spurs  and  ratchet-wheel  in 
the  direction  of  the  arrow,  and  the  cam-plate  is  also  turned  in 


408 


mason's  self-acting  mule. 


the  same  direction,  by  the  catch  or  hand  (v);  this  motion  is  gra- 
dually arrested  by  the  enlarged  or  scroll-form  of  the  cam-plate, 
which  forces  out  a  friction  arm  (6'),  one  end  of  which  is  jointed 
at  (a'),  to  one  arm  of  a  lever  (F^)  attached  to  the  rock-shaft  (w), 
the  other  arm  of  this  lever  being  connected  with  the  friction  arm 
(Z')  by  a  helical  spring  (S),  it  will  therefore  be  perceived,  that  as 
the  friction- arm  is  forced  out  by  the  cam-plate,  the  tension  of  the 
spring  increases  the  friction  of  the  brake  on  the  periphery  of  the 
cam-plate,  which  gradually  arrests  the  motion  of  all  the  parts  in 
connection  with  the  rack  (W'),  and  of  necessity  the  spindles. 
When  these  parts  are  arrested,  the  rock-shaft  (n)  is  turned  in  the 
opposite  direction,  and  carries  with  it  the  cam-plate,  ratchet- 
wheel,  and  spur-wheel  by  the  pressure  of  the  brake,  and  of  ne- 
cessity reverses  the  motion  of  the  rack  and  spindles  to  uncoil 
the  threads  from  the  spindles.  At  the  end  of  this  motion,  the 
catch  (u)  of  the  cam-plate  is  liberated  from  the  ratchet-wheel 
(H^)  by  a  spur  (x)  of  a  lever  (?/)  jointed  at  (14),  to  the  arm  (F^) 
of  the  rock-shaft  (n),  the  spur  being  forced  on  to  the  back  end 
of  the  catch  by  the  rotation  of  the  rock-shaft,  the  lever  (?/)  hav- 
ing a  slot  in  it  which  turns  and  slides  upon  a  permanent  rod  {z). 
This  reversed  motion  of  the  rock-shaft  (n)  is  effected  by  a  crank 
motion  in  the  following  manner,  viz. :  The  pinion  (D)  on  the  second 
fast  pulley  (A')  communicates  motion  by  the  train  of  Avhcels  (B^ 
and  R^)  to  the  wheel  (Q^)  in  the  direction  of  the  arrow,  and 
this  wheel  carries  a  crank  pin  (7i'),  that  works  in  a  slot  (/t^)  of  a 
connecting  rod  (0^),  jointed  to  a  curved  arm  (K^)  that  vibrates 
on  a  fixed  stud-pin  (15),  and  this  arm  has  a  slot  in  it  which  works 
a  slide  (e'),  for  the  purpose  of  graduating  the  backing  off  motion, 
and  to  this  slide  is  jointed  another  connecting  rod  (J^),  the  other 
end  of  which  is  jointed  to  the  arm  (I^)  of  the  rock-shaft  (/;).  At 
the  time  that  the  driving  belt  is  shifted  to  the  second  fast  pulley 
(A^),  which  takes  place  while  the  momentum  of  the  spindles  pre- 
pares the  parts  for  the  backing-off  motion,  the  crank  pin  (h^)  is 
at  (7i^),  a  little  above  a  line  passing  from  the  centre  of  the  wheel 
to  the  junction  of  the  connecting  rod  (0^)  and  the  arm  (K^),  so 
that  the  crank  pin  on  this  wheel  can  move  around  to  the  position 
represented  in  Fig.  2,  before  it  begins  to  draw  the  connecting  rod, 
to  give  time  for  completing  the  preparation  of  the  parts  for  back- 
ing off.  In  rotating  from  (A')  to  {h*),  the  crank  pin  carries  the 
connecting  rod  the  required  distance  to  give  the  required  backing- 
off  motion  to  the  spindles  to  uncoil  the  threads,  and  at  the  same 
time  depresses  the  faller  to  guide  the  threads  to  the  cops,  prepa- 
ratory to  winding  on  by  means  of  the  coping  rail  or  former  (G^), 


■ 


mason's  self-acting  mule. 


409 


one  end  of  which  is  connected  by  a  slot  with  a  wrist  (q)  on  an 
arm  (F^)  of  the  rock-shaft  (n),  the  elevation  of  which  by  the  back- 
ing-olF  motion  of  the  rock-shaft  (n)  depresses  the  faller.  So  soon 
as  the  connecting  rod  (o^)  has  been  carried  to  the  point  (h*)  by 
the  crank  pin,  which  is  the  extent  of  the  backing-olF  motion,  the 
catch  lever  (U^)  takes  hold  of  the  pin  (13)  on  the  arm  (K^),  and 
there  holds  all  the  parts  of  the  backing-ofF  operation  until  re- 
leased towards  the  end  of  the  running- in  motion  of  the  carriage, 
the  liberation  of  the  parts  being  then  effected  by  means  of  a  pin 
(P)  on  the  arm  (L^)  on  the  shaft  (K')  of  the  wheel  (F'),  which 
runs  in  the  carriage.  So  long  as  the  backing-ofF  apparatus  is 
held  by  the  catch  lever  (U^),  the  crank  pin  (A^)  can  revolve  freely, 
the  slot  in  the  connecting  rod  (0^)  admitting  of  this.  When  the 
backing-oif  apparatus  is  liberated,  it  falls  back  to  the  position 
indicated  in  the  drawings  by  the  weight  of  the  coping  rail  and 
the  other  parts  attached  to  the  rock-shaft  ;  and  to  prevent  jar, 
this  return  motion  of  the  parts  is  eased  off  by  the  connecting  rod 
(0^),  coming  against  the  crank  pin  (h^)  at  the  point  (h^),  the  power 
required  to  turn  this  train  of  wheels  in  the  reverse  direction  being 
sufficient  to  ease  off  and  gradually  arrest  the  moving  parts  without 
jar.  This  return  motion  of  the  backing-off  apparatus  at  the  same 
time  arrests  the  second  fast  pulley  (A^)  and  the  train  of  wheels 
in  connection  with  it,  by  means  of  a  brake  {j'-)  connected  by  the 
arm  (T^),  and  link  (S^)  with  the  arm  (K^)  of  the  backing-off  ap- 
paratus, and  the  train  of  wheels  and  the  connection  of  the  brake 
are  so  regulated  as  to  stop  the  crank  pin  (7i^)  at  the  point  (h^), 
where  it  is  required  to  be  when  the  second  series  of  motions  is 
commenced.  The  link  (S^),  and  the  connecting  rod  (J^),  are  pro- 
vided with  adjusting  screws  for  the  proper  adjustment  of  all  these 
parts. 

As  the  backing-off  motion  must  be  gradually  decreased  ^s  the 
cop  is  formed  and  increased  in  length,  the  vibrating  motion  of 
the  rock-shaft  is  gradually  shortened  by  means  of  the  slide  (e^) 
in  the  arm  (K^)  to  which  the  connecting  rod  (J^)  is  jointed. 

For  this  purpose,  the  slide  is  attached  to  a  chain  (c?'),  which 
passes  over  the  upper  end  of  the  arm,  and  is  gradually  wound 
upon  the  arbor  (e^'j  of  a  cog-wheel  (L^)  that  gears  into  a  pinion 
(/')  of  a  ratchet-wheel  (N^),  which  receives  motion  from  the 
vibration  of  the  arm  (K^)  of  the  backing-off  apparatus,  by  a  hand 
or  catch  (M^)  jointed  thereto  at  (g^).  It  will  be  evident  that,  as 
the  slide  is  drawn  up  by  the  chain  towards  the  axis  of  motion  of 
the  arm  (K^),  the  motion  of  the  connecting-rod  (P)  will  be  di- 
minished, and  with  it  the  motion  of  the  backing-off  apparatus. 
27 


410 


mason's  self-acting  mule. 


This  completes  the  second  series  of  motions,  and  the  mule  is 
then  in  a  condition  to  commence  the  third  serifs. 

When  the  clutch  (D^)  at  the  end  of  the  backing-off  motion 
clutches  the  pinion  (E'),  it  begins  to  turn,  -which  communicates 
motion  to  the  cog-wheel  (F')  on  the  shaft  (K') ;  and  to  the 
periphery  of  this  wheel  at  (G'),  is  jointed  a  connecting-rod  (H'), 
the  other  end  of  which,  at  (I'),  is  jointed  to  a  horizontal  sliding- 
rack  (V)  that  runs  on  ways  (W),  that  carries,  by  means  of  the 
pinion  (U),  the  train  of  wheels  that  communicate  motion  to  the 
carriage.  The  wheel  (F")  is  carried  but  part  of  a  revolution 
(nearly  one-half)  in  one  direction  by  its  connection  with  the 
second  driving-pulley  (A'),  when  the  clutch  (D^)  is  closed,  which 
gives,  by  the  crank-motion  in  consequence  of  the  connection 
above  pointed  out,  the  peculiar  running-in  motion  to  the  carriage, 
as  pointed  out  in  the  description  of  the  general  characteristics  of 
this  invention;  and,  as  the  carriage  approaches  the  end  of  its 
running-in  motion,  the  jiinion  (E')  is  unclutched  by  the  reversed 
action  of  the  shipper-lever  (C''),  this  reversed  motion  of  the  ship- 
per and  its  appendages  being  effected  by  the  pin  (e)  on  the  arm 
(L^J  of  the  shaft  (K')  of  the  wheel  (F'),  this  pin  (e)  being  on  the 
side  of  the  shaft  (KM  opposite  to  the  pin  (a)  which  first  ships  it. 
The  unclutching  of  the  pinion  (E')  leaves  the  wheel  (F')  free  to 
be  turned  back  by  the  reversed  motion  of  the  rack  (V)  by  the 
train  of  wheels  which  run  out  the  carriage  in  the  first  series  of 
motions. 

As  the  carriage  is  run  in  by  the  means  just  described,  the 
spindles  must  be  turned  to  wind  up  the  threads  which  have  been 
spun  during  the  first  series  of  motions,  and  this  is  effected  by 
means  of  the  top  sliding-rack  (W'),  by  which  the  backing-off 
motion  is  given,  and  which  is  placed  on  top  of  the  main  rack  (V). 
The  oonnection  of  this  rack  (W)  with  the  spindles,  by  means 
of  the  friction-clutch,  having  been  described,  it  is  only  necessary 
to  describe  the  manner  in  which  the  winding-on  motion  is  com- 
municated to  it  by  the  main  rack  (V),  and  the  manner  in  which 
this  motion  is  varied  and  regulated  to  correspond  with  the  vary- 
ing size  of  the  cops  as  they  are  formed.  To  the  upper  rack  (W'), 
and  near  one  end  of  it,  is  jointed  a  lever  (ra'),  to  the  short  arm 
of  which  is  attached  a  chain  (/'),  which  thence  passes  around  a 
pulley  [k^)  that  turns  on  a  stud-pin  projecting  from  the  side  of 
the  main  rack  (V),  the  other  end  of  the  said  chain  being  attached 
to  the  smallest  diameter  of  a  scroll-cam  (n')  connected  with  the 
end  of  the  main  rack  (V).  From  this  arrangement  it  will  be 
obvious  that  if  the  cam  (n)  be  prevented  from  turning  on  its 


mason's  self-acting  mule. 


411 


axis,  the  motion  of  the  main  rack  (V)  will  carry  the  top  rack  in 
the  same  direction  and  Avith  the  same  varying  velocity,  which 
would  give  to  the  spindle  a  winding-on  motion  corresponding 
with  the  running-in  motion  of  the  carriage,  such  as  would  be 
requii'ed  if  the  cops  were  to  be  formed  cylindrical  and  did  not 
vary  in  diameter  ;  but  such  is  not  the  case,  as  clearly  pointed 
out  in  the  general  description.  To  give  the  varying  motion 
required  and  fully  pointed  out  above,  the  scroll-cam  (n^)  is 
attached  to  and  turns  with  a  wheel  {v)  on  the  stud-pin  (P)  on 
the  main  rack  (V),  and  to  this  wheel,  at  (w),  is  attached  a  chain 
(x^),  which,  after  passing  around  a  portion  of  the  circumference 
thereof,  is  attached  by  a  link  (?/')  to  a  slide  (2")  that  travels  on  a 
screw  (a")  that  turns  in  the  arm  (V^)  of  a  rack-frame  (V^),  the 
lower  end  of  the  said  arm  being  jointed  to  another  arm  of  equal 
length  (W^)  that  vibrates  on  the  stud-pin  (I')  on  which  turn  the 
wheel  [v^)  and  the  cam  f?i'),  so  that  when  the  slide  (2'^)  is  at  the 
lower  end  of  the  arm  (V^),  that  end  of  the  chain  (x^)  which  is 
attached  to  the  slide,  during  the  movements  of  the  main  rack, 
will  not  communicate  motion  to  the  wheel  (w")  and  cam  (n^) ; 
hence  the  motions  of  the  two  racks  (V)  and  (W),  will  correspond 
and  give  to  the  spindles  the  motion  required  for  winding  the 
threads  on  the  naked  spindles,  and,  as  the  base  of  the  cops  is 
increased  in  diameter,  the  slede  (2'')  is  drawn  up  towards  the 
axis  of  motion  of  the  arm  (V^)  to  decrease  the  motion  of  that 
end  of  the  chain  (x^)  attached  to  it,  which  will  cause  the  wheel 
and  cam  to  turn  on  their  axis,  and  thus  give  out  the  chain  (Z'), 
thereby  giving  to  the  top  rack  (W),  and,  consequently,  to  the 
spindles,  a  gradually  reduced  motion  relatively  to  the  main  rack 
to  correspond  with  the  increased  diameter  of  the  base  of  the 
cops.  The  motion  required  is  given  to  the  slide  (z^^)  by  the 
vibrations  of  the  rock-frame  (V^j,  the  screw  (a")  that  operates 
the  slide  being  connected  by  a  train  of  cog-wheels  e", 
7i",  j^^),  with  a  horizontal  ratchet-wheel  which  turns 
freely  by  the  rucking  motion  of  the  frame  (V^)  in  one  direction, 
and  which,  therefore,  does  not  turn  the  screw  but  which  is  pre- 
vented from  turning  in  the  opposite  direction  (during  the  running- 
in  motion  of  the  carriage)  by  a  catch  or  pawl  (r")  to  turn  the 
said  screw. 

Whenever  the  tension  of  the  threads  in  winding  on  is  too 
great,  it  bears  down  the  counter-faller  (not  represented  in  the 
drawings),  the  arm  of  which  in  the  running-in  motion  of  the 
carriage  sti'ikes  an  arm  (S")  of  what  is  termed  a  butterfly, 
that  turns  on  a  stud  pin  (^''j,  on  which  the  catch  or  hand  (r'^) 


1 


412  mason's  self-acting  mule. 

of  the  ratchet  (P)  also  turns,  and  with  which  it  is  connected  by 
a  spring  (see  Fig.  1),  and  throws  it  into  the  teeth  of  the 
ratchet-wheel — the  wheel  being  thus  held,  the  farther  vibration 
of  the  rock-frame  turns  the  screw,  and  carries  up  the  slide  to  re- 
duce the  motion  of  the  spindle,  and  on  the  return  motion  of  the 
carriage,  the  hand  or  catch  (r")  is  thrown  out  of  the  teeth  of  the 
ratchet-wheel  by  the  arm  of  the  counter-faller,  which  then  comes 
in  contact  with  another  arm  (f^)  of  the  butterfly,  the  end  of  which 
extends  lower  down  than  the  arm  (S^),  and  low  enough  to  be 
struck  by  the  arm  of  the  counter-faller,  when  it  is  not  under  the 
action  of  the  tension  of  the  threads.  The  catch  or  hand  then 
remains  out,  until  the  tension  of  the  threads  again  requires  the 
motion  of  the  spindle  to  be  reduced.  The  butterfly  is  connected 
with  a  hand-catch  lever  (m^)  that  turns  on  a  stud-pin  (m^),  by 
which  the  attendant  can  throw  the  butterfly  in  and  out  of  play. 
So  soon  as  the  base  of  the  cop  has  been  formed,  the  scroll  form 
of  the  cam  (m^)  gives  the  regular  varying  motions  to  the  spin- 
dles to  wind  the  cone  of  the  cops,  as  fully  pointed  out  in  the 
general  description. 

It  has  been  stated  that  in  finishing  the  cops,  the  threads  are 
wound  on  harder  at  the  point  of  the  cops — this  is  effected  in  the 
following  manner.  On  the  shaft  (e")  which  regulates  the  back- 
ing-off  motion  as  described  above,  there  is  a  hub  (^^)  from  which 
projects  a  crank  arm  (^'),  to  the  pin  (S')  of  which  is  jointed  by 
a  link  (r^),  a  chain  (|j>'),  the  other  end  of  which  is  jointed  by  a 
link  (0^)  to  the  long  arm  of  the  lever  (w'),  which  forms  the  con- 
nection between  the  top  rack  (W)  and  the  chain  (Z'),  which  forms 
the  connection  between  the  top  and  main  racks.  This  shaft,  as 
heretofore  described,  is  connected  Avith  the  ratchet-wheel  (N^) 
which  is  operated  by  the  catch  or  hand  (M^)  of  the  lever  (K^)  of 
the  backing-off"  apparatus,  and  the  chain  {p'^)  is  of  such  length 
that  it  is  wound  up  by  the  rotation  of  the  shaft,  until  towards 
the  completion  of  the  cops,  at  which  time  it  is  drawn  sulRciently 
tight  to  strike  against  a  permanent  arm  (m')  towards  the  end  of 
the  winding-in  motion,  which  causes  the  lever  (m^)  to  turn  on  its 
axis,  and  by  its  connection  to  draw  up  the  chain  (Z'),  and  hence 
to  increase  the  velocity  of  the  rack  (W"),  and,  therefore,  the  ro- 
tation of  the  spindles  which  winds  the  threads  on  tighter — this 
operation  gradually  increases  to  the  completion  of  the  cops.  On 
this  same  shaft  (e'^)  is  placed  the  coping  arm  (?/^),  the  periphery 
of  which  acts  on  the  lever  (x^),  to  which  the  coping  rail  or  former 
(G^)  is  jointed  at  (r)  in  manner  Avell  known  to  those  acquainted 
with  the  construction  of  self-acting  mules,  and  which,  therefore, 


V 


mason's  self-acting  mule. 


413 


needs  not  to  be  described.  This  completes  the  whole  series  of 
motions,  but  it  will  be  obvious  that  when  one  set  of  cops  has  been 
completed,  the  parts  employed  in  giving  the  progressive  move- 
ments, such  as  the  shaft  (e")  that  rotates  the  coping  or  forming 
cam  (Y^)  winds  the  chain  which  carries  the  slide  (e^)  of  the  back- 
ing-olf  apparatus,  and  the  crank  arm  (i')  that  winds  the  chain  (p') 
to  increase  the  tension  of  the  threads  in  finishing  the  points  of 
the  cop,  and  also  the  ratchet-wheels  (V)  which  governs  the  mo- 
tions of  the  slide  (2'')  on  the  arm  (V^),  by  which  the  winding-on 
motion  of  the  spindles  is  regulated  to  form  the  base  of  the  cops, 
are  to  be  turned  back  by  hand  to  their  original  positions  by  the 
attendant  preparatory  to  commencing  a  new  set  of  cbps. 

I  have  thus  described  the  general  character  of  the  invention, 
and  the  manner  of  constructing  and  using  the  same,  but  before 
pointing  out  what  I  claim  as  my  invention,  I  wish  it  to  be  dis- 
tinctly understood  that  I  do  not  limit  myself  to  the  precise  form 
and  construction  of  the  various  parts  employed,  or  to  the  pre- 
cise arrangement  described,  as  I  consider  all  mechanical  equiva- 
lents as  within  the  limits  of  my  invention. 

What  I  claim,  therefore,  as  my  invention,  and  desire  to  secure 
by  letters  patent  is — First,  the  disconnecting  of  the  mechanism 
employed  in  running  out  the  carriage  and  turning  the  draw  roll- 
ers, from  the  mechanism  which  gives  the  whirling  or  spinning 
motion  to  the  spindles,  when  the  driving  power  is  shifted  from 
these  the  first  series  of  motions,  to  enable  the  spindles  to  con- 
tinue their  motion  by  inertia,  independent  of  the  other  motions, 
by  means  of  the  clutch  box  (or  its  equivalent)  which  forms  the 
connection  between  the  three  movements  constituting  the  first 
series  of  motions,  whereby  the  momentum  of  the  spindles  can  be 
employed  for  preparing  the  parts  for  the  backing-off  motion, 
substantially  as  described.  Second.  The  method  of  preparing 
the  parts  for  the  backing-off  motion  by  means  of  the  momentum 
of  the  spindles,  by  connecting  them  with  the  backing-olf  appa- 
ratus by  means  of  the  friction  clutch,  or  any  equivalent  there- 
for, substantially  as  described.  Third.  The  backing-off  appa- 
ratus consisting  of  the  combination  of  the  top-sliding  rack,  which 
communicates  motion  to  the  spindles,  the  rocking  shaft  with  its 
cam  and  spring  brake  and  other  appendages,  and  the  connecting 
rod  operated  by  the  crank,  all  substantially  as  described.  Fourth. 
The  method  of  decreasing  the  backing-off  motion  to  correspond 
Avith  the  increased  length  of  the  cops,  by  means  of  the  slide  in 
the  intermediate  arm  of  the  connecting  rod  (between  the  two 
sections  of  the  connecting  rod),  by  means  of  which  the  rocking 


414 


mason's  self-acting  mule. 


motion  of  the  rock-shaft  is  gradually  decreased,  substantially  as 
described.  Fifth.  Combining  the  train  of  wheels  which  actuates 
the  backing-off  motion  of  the  carriage,  by  means  of  a  clutch 
substantially  as  herein  described,  which  admits  of  the  necessary 
backing-ofl'  motion  before  the  tooth  of  the  clutch  starts  the  car- 
riage,  whether  this  be  effected  by  a  clutch  or  by  any  other  means 
substantially  the  same.  Sixth.  Running  in  the  carriage  by 
means  of  a  crank  motion  which  actuates  a  sliding  rack  that  com- 
municates the  desired  motion  to  the  carriage,  so  as  to  start  and 
arrest  it  gradually,  substantially  as  described,  to  avoid  any  sud- 
den strain  or  jar  upon  the  threads.  Seventh.  The  method  of 
communicating  the  winding-on  motion  to  the  spindles  from  the 
main  rack,  which  runs  in  the  carriage  by  combining  the  said  main 
rack  with  the  top-sliding  rack  by  means  of  a  chain  and  scroll 
cam,  or  their  equivalents,  by  means  of  which  combination  in 
connection  with  the  form  of  the  cam,  the  motions  of  the  spin- 
dles so  correspond  with  that  of  the  carriage,  as  to  wind  the 
threads  on  the  conical  form  of  the  cops  as  described.  Eighth. 
The  method  of  varying  the  winding-on  motion  of  the  spindles  to 
form  the  base  of  the  cops,  by  means  of  the  slide  and  chain  which 
vary  the  motions  of  the  wheel  that  is  attached  to,  and  which 
rotates  the  scroll  cam  substantially  as  described,  whether  the 
slide  be  opei-ated  by  the  vibration  of  the  arm  on  which  it  slides, 
or  by  any  other  means  substantially  as  herein  described.  Ninth. 
The  method  of  regulating  the  motion  of  the  slide  that  varies  the 
motions  of  the  scroll  cam  of  the  winding-on  motion,  by  means 
of  what  is  termed  the  butterfly  and  its  appendages,  when  this  is 
acted  upon  by  the  counter-faller,  operated  by  the  tension  of  the 
threads,  substantially  as  described.  And,  Tenth.  The  method 
of  winding  on  the  threads  tighter  at  the  points  of  the  cops, 
when  finishing  them  by  means  of  the  apparatus,  which  gives  to 
the  top-sliding  rack,  an  increased  motion  towards  the  end  of  the 
operation,  the  said  apparatus  consisting  of  a  chain  which  is  con- 
nected with  the  chain  that  forms  the  connection  between  the 
main  and  top  racks,  and  which  is  gradually  wound  up,  and  strikes 
against  an  arm  towards  the  end  of  the  operations  of  the  mule, 
to  shorten  the  connection  between  the  two  racks,  and  thus  in- 
crease the  winding-on  motion  of  spindles  as  described. 


NIAGARA  THROSTLE,  OR  McCULLEY'S 
SPINNING  FRAME. 

PLATES  VII.  VIII. 

This  machine  possesses  the  following  advantages  over  all  other 
kinds  of  Thi'ostle  or  common  Ring  Spinning  Frames : — 

1.  A  saving  of  one-half  THE  POWER  consumed  by  the  Spin- 
ning Frames  now  in  general  use. 

2.  It  occupies  one-fifth  less  space. 

3.  It  is  operated  with  one-third  less  LABOR  compared  with 
its  product. 

4.  It  requires  but  one-half  the  Oil  of  other  Spinning. 

5.  All  Banding  is  entirely  dispensed  with. 

6.  The  Repairs  are  not  one-half  that  of  frames  running  with 
bands. 

7.  It  is  not  affected  by  change  of  weather;  therefore  it  uses  a 
uniform  amount  of  power. 

8.  It  can  be  operated  at  much  greater  speed  and  without  a 
corresponding  increase  of  power  and  wear  and  tear. 

9.  It  gives  a  stronger  and  more  uniform  motion  to  the  spindle 
and  a  more  even  twist  to  the  thread. 

10.  It  combines  superior  advantages  for  Spinning  fine  Worsted, 
with  great  speed  and  perfection. 

11.  It  is  particularly  well  adapted  for  doublers  and  twisters  for 
thread,  and  many  are  now  in  operation. 

There  are  many  minor  advantages  with  this,  over  all  other 
spinning  now  in  use.  It  does  not  throw  olf  the  oil — it  is  a  much 
more  durable  machine,  and  gets  rid  of  bands  with  all  their  ex- 
pense, annoyances,  imperfections  and  uncertainties.  It  does  not 
require  that  attention  and  skill  in  the  overseer  to  regulate  it, 
after  it  is  adjusted  to  give  the  twist  intended ;  and  when  once 
adjusted,  so  it  will  remain  and  continue  to  operate.  If  required, 
the  Spindles  may  be  driven  10,000  revolutions  per  minute. 
Nearly  two-thirds  the  power  of  a  Cotton  Mill  is  wanted  to  drive 
the  spinning,  and  the  great  saving  in  power  by  this  frame  reduces 
the  weight  and  expense  of  main  gearing,  shafting,  pulleys,  and 


416 


NIAGARA  THROSTLE. 


belts  correspondingly.  It  can  be  readily  changed  from  coarse 
to  fine  yarn.  Either  side  of  this  frame  may  be  operated  indepen- 
dently of  the  other,  and  stopped  at  pleasure,  without  affecting 
the  operation  of  the  other  side. 

These  are  believed  to  be  fair  statements  of  facts,  which  the 
operation  of  this  machine  with  more  than  two  years  practical 
test  fully  confirms. 

These  Spinning  frames  may  be  seen  in  operation,  in  many 
sections  of  the  country. 

The  novelty  consists  in  the  mode  of  driving  the  Spindles, 
Flyers,  and  Bobbins  by  friction  pulleys  instead  of  bands  (the 
old  way),  as  invented  and  patented  by  Francis  McCulley,  Jr. 
The  lithograph  represents  a  Ring  Spinning  Frame,  in  which  the 
usual  cylinders  and  bands  are  dispensed  with,  and  the  friction 
pulleys  are  introduced.  The  invention  is  as  applicable  to  driving 
flyers,  and  also  for  Douhlers  and  Twisters,  and  Worsted  Frames. 
It  may  be  applied  to  all  kinds  of  throstle  spinning,  with  similar 
advantages.  It  is  very  largely  in  operation,  and  with  the  univer- 
sal testimony  of  those  using  them,  that  the  motion  to  the  spindle 
is  stronger,  more  regular  and  uniform  driven  by  friction  pulleys, 
than  when  driven  by  bands.  There  is  a  whirl  made  fast  to  the 
spindle,  the  underside  of  which  is  covered  with  leather,  and  rests 
upon  the  periphery  of  the  pulley.  These  leathers  will  last  for 
many  years,  and  the  spindles  and  beai-ings  wear  but  very  little, 
having  no  bands  pulling  them. 

Fig.  4,  Plate  VIII.  is  an  end  elevation,  showing  the  arrange- 
ment for  the  gears  and  belts  for  driving  the  rolls  and  lifting  motion 
for  the  rails. 

Fig.  1,  Plate  VII.  is  a  front  elevation,  showing  the  rolls, 
spindles,  and  an  edge  view  of  the  friction-disks  for  driving  the 
spindles.  These  disks  and  the  whirls  running  upon  them  consti- 
tute the  parts  patented  by  McCulley. 

Fig.  3,  Plate  VIII.  is  a  vertical  section  of  the  machine  through 
the  centre  of  one  section,  showing  the  roller-stands ;  the  manner 
of  weighing  top-rolls  by  the  weights ;  the  bearings  for  the  side- 
shafts,  stands  for  the  spindles,  guide-rod  for  raising  top  or  ring 
rail. 

Fig.  2,  Plate  VIII.  is  an  end  elevation. 

Further  information  may  be  obtained  of  the  Agents,  Miner  & 
Pitman,  171  Milk  Street,  Boston,  Mass.,  or  of  Arthur  M.  East- 
man, of  Boston,  the  proprietor  of  the  patent,  and  who  has  been 
chiefly  instrumental  in  bringing  this  admirable  machine  to  its 
present  state  of  perfection. 


Pl.itc  III 


FOLDOUT  BLANK 


e®TT®!M  SlPDKIfSIEIS. 


INDEX 


TO  THE 


PRACTICAL  MODE  CALCULATOR. 


BT 

OLIVEE  BYRNE, 

CIVIL,  MILITARY,  AND  MECHANICAL  ENGINEER. 


PHILADELPHIA: 
PUBLISHED  BY  HENRY  CAREY  BAIRD, 

(SUCCESSOR  TO  E.  L.  CAREY,) 

SOUTH-EAST  CORNER  MARKET  AND  FIFTH  STREETS. 

1851. 


INDEX. 


Abbreviation  of  the  reduction  of  decimals,  1 7. 

Abrasion,  limits  of,  301. 

Absolute  resistances,  2S8. 

Absolute  strength  of  cylindrical  columns,  274. 

Accelerated  motion,  386. 

Accelerated  motion  of  wheel  and  axle,  419. 

Acceleration,  415. 

Acceleration  and  mass,  422. 

Actual  and  nominal  horse  power,  240. 

Addition  of  decimals,  22. 

Addition  of  fractions,  20. 

Adhesion,  297. 

Air,  expansion  of,  by  heat,  173. 

Air  that  passes  through  the  fire  for  each  horse 

power  of  the  engine,  210. 
Air,  water,  and  mercury,  355. 
Air-pump,  254. 

Air-pump,  diameter  of,  eye  of  air-pump  cross 
head,  145. 

Air-pump  machinery,  dimensions  of  several 

parts  of,  144. 
Air-pump  strap  at  and  below  cutter,  147. 
Air-pump  studs,  144. 
Ale  and  beer  measure,  8. 
Algebra  and  arithmetic,  characters  used  in,  12. 
Algebraic  quantities,  134. 
Alloys,  strength  of,  287. 
Ambiguous  cases  in  spherical  trigonometry, 

381. 

Amount  of  efifective  power  produced  by  steam, 
266. 

Anchor  rings,  90. 
Angle  iron,  91,  408,  409,  410. 
Angles  of  windmill  sails,  445. 
Angles,  measurement  of,  by  compasses  only, 
382. 

Angular  magnitudes,  359. 

Angular  magnitudes,  how  measured,  373. 

Angular  velocity,  412. 

Apothecaries'  weight,  6. 

Apparent  motion  of  the  stars,  353. 

Application  of  logarithms,  334. 

Approximating  rule  to  find  the  area  of  a  seg- 
ment of  a  circle,  67. 

Approximations  for  facilitating  calculations, 
55. 

Arc  of  a  circle,  to  find,  49. 
Arc  of  one  minute,  to  find  the  length  of,  361. 
Arc,  the  length  of  which  is  equal  to  the  ra- 
dius, 357. 
Architecture,  naval,  453. 
Arcs,  circular,  to  find  the  lengths  of,  68. 
Area  of  segment  and  sector  of  a  circle,  51. 
Area  of  steam  passages,  220. 
Areas  of  circles,  57. 

Areas  of  segments  and  zones  of  circles,  64, 

05,  66,  67. 
Arithmetic,  10. 

Arithmetical  progression,  to  find  the  square 

root  of  numbers  in,  126. 
Arithmetical  solution  of  plane  triangles,  366. 
2x2 


Arithmetical  proportion  and  progression,  35 
to  38. 

Ascent  of  smoke  and  heated  air  in  chimneys, 
208. 

Atmospheres,  elastic  force  of  steam  in,  195, 
196. 

Atmospheric  air,  weight  of,  356. 

Average  specific  gravity  of  timber,  396. 

Avoirdupois  weight,  6. 

Axle  and  wheel,  417. 

Axle  of  locomotive  engine,  168,  169. 

Axle-ends  or  gudgeons,  301. 

Axles,  friction  of,  298,  300. 

Balls  of  cast  iron,  407. 
Bands,  ropes,  &c.,  267. 
Bar  iron,  400. 
Beam,  151. 

Beam,  the  strongest,  276. 

Bearings  of  water  wheels,  285. 

Bearings  or  journals  for  shafts  of  various 

diameters,  287. 
Beaters  of  threshing  machine,  445. 
Before  and  behind  the  piston,  232. 
Blast  pipe,  171. 
Blistered  steel,  281. 
Blocks,  cords,  ropes,  shelves,  428. 
Bodies,  cohesive  power  of,  175. 
Bodies  moving  in  fluids,  324. 
Boiler,  171. 

Boiler  plate,  experiments  on,  at  high  tempe- 
ratures, 220. 
Boiler  plates,  403. 
Boilers,  256  and  257. 

Boilers  of  copper  and  ii-on,  diminution  of 

the  strength  of,  219. 
Boilers,  properties  of,  215. 
Boilers,  strength  of,  218. 
Bolts  and  nuts,  406. 
Bolts,  screw  and  rivet,  220. 
Boring  iron,  445. 

Bossut  and  Michelloti,  exiieriments  on  the 

discharge  of  water,  319. 
Boyle  of  Cork,  200. 
Bramah's  press,  427. 
Branch  steam-pipe,  148. 
Brass,  copper,  iron,  properties  of,  280. 
Brass,  round  and  square,  408. 
Breast  wheels,  328. 

Breast  and  overshot  wheels,  maximum  ve- 
locity of,  443. 

Buckets  and  shrouding  of  water  wheels,  446. 

Building,  to  support  with  cast  iron  columns, 
293. 

Bushel,  5. 

Butt  for  air-pump,  146. 
Butt,  thickness  and  breadth  of,  143. 
Butt,  to  find  the  breadth  of,  141. 
Byrne's  logarithmic  discovery,  340. 
Byrne's  theory  of  the  strength  of  materials, 
272. 

5G9 


570 


INDEX, 


Calculation  in  the  art  of  ship-building,  453 
to  500. 

Canvas  of  vessels,  488,  500. 

Carriages,  motion  of,  on  inclined  planes,  429. 

Carriages  travelling  on  ordinary  roads,  307. 

Carrier  or  intermediate  wheels,  434. 

Carts  on  ordinary  roads,  311. 

Cases  in  plane  trigonometry,  363. 

Cast  iron,  174. 

Cast  iron  pipes,  404. 

Centre  of  effort  of  sails,  483,  490. 

Centre  of  gravity,  175. 

Centre  of  gravity  of  displacement  of  a  ship, 

456,  457,  458. 
Centre  of  gyration,  180. 
Centre  of  oscillation,  187. 
Centres  of  bodies,  386. 

Centres  of  gravity,  gyration,  percussion  os- 
cillation, 391. 
Centripetal  and  centrifugal  forces,  178,  450. 
Chain  bridge,  412. 
Chimney,  171,  208,  257. 
Chimney,  size  of,  212. 

Chimney,  to  what  height  it  may  be  carried 

with  safety,  212. 
Circle,  calculations  respecting,  48,  49,  50,  53. 
Circle  of  gyration  in  water  wheels,  444. 
Circles,  57  to  61. 
Circles,  areas  of,  57  to  63. 
Circular  arcs,  68. 
Circular  motion,  422. 
Circular  parts  of  spherical  triangles,  375. 
Circumference  of  a  circle  to  radius  1,  361. 
Circumferences  of  circles,  57. 
Cloth  measure,  7. 
CoefBeieut  of  efflux,  314. 
Coefficients  of  friction,  299. 
Cohesive  strength  of  bodies,  how  to  find,  281. 
Collision  of  railway  trains,  452. 
Columns,  comparative  strength  of,  294. 
Combinations  of  algebraic  quantities,  134. 
Common  fractions,  15. 
Common  materials,  2S0- 
Complementary  and  supplementary  arcs,  374. 
Compound  proportion,  14. 
Condenser,  226. 
Condensing  water,  223. 
Conduit  pipes,  discharge  by,  322. 
Cone,  82. 

Conical  pendulum,  185  to  187. 
Connecting  rod,  140,  141,  253. 
Continuous  circular  motion,  432. 
Contraction  by  efflux,  316. 
Contraction  of  the  fluid  vein,  313. 
Contractions  in  the  calculation    of  loga- 
rithms, 348. 
Copper  boilers,  219. 
Copper,  iron,  and  load,  405. 
Cosine,  to  find,  361. 

Cosines,  contangents,  &c.,  for  every  degree 

and  minute  in  the  quadrant,  540  to  576. 
Cosines,  natural,  411. 

Cover  on  the  exhausting  side  of  the  valve, 

in  parts  of  the  length  of  stroke,  231. 
Cover  on  the  steam  side,  226. 
Crane,  427. 

Crane,  sustaining  weight  of,  285. 
Crank  at  paddle  centre,  135. 
Crank  axle,  diameter  of  the  outside  bearings 
of,  168. 


Crank  axle  of  locomotive,  169. 

Crank  pin,  170,  252. 

Crank  pin  journal,  252. 

Crank  pin  journal,  to  find  the  diameter  of,  139. 

Crank  pin  journal,  to  find  the  length  of,  139. 

Cross  head,  252. 

Cross  head,  to  find  the  breadth  of  eye  of,  139. 
Cross  head,  to  find  the  depth  of  eye  of,  139. 
Cross  multiplication,  27. 
Cross  tail,  253. 
Cube,  79. 

Cube  and  cube  roots  of  numbers,  100  to  116. 
Cube  root  of  numbers  containing  decimals, 
128. 

Cube  root,  to  extract,  32. 
Cubes,  397  to  400. 
Cubes,  to  extend  the  table  of,  128. 
Curve,  to  find  the  length  of,  by  construction, 72. 
Curves,  to  find  the  areas  of,  453. 
Cuttings  and  embankments,  97. 
Cylinder  side  rods  at  ends,  to  find  the  diame- 
ter of,  143. 
Cylinders,  80,  397  to  400. 
Cylinders  of  east  iron,  404. 

Dams  inclined  to  the  horizon,  316. 

Decimal  approximations  for  facilitating  cal- 
culations, 55. 

Decimal  equivalents,  56. 

Decimal  fractions,  22. 

Decimal  fractions,  table  of,  73. 

Decimals,  addition  of,  22. 

Decimals,  division  of,  24. 

Decimals,  multiplication  of,  23. 

Decimals,  reduction  of,  25,  26. 

Decimals,  rule  of  three  in,  27. 

Decimals,  subtraction  of,  23. 

Deflection  of  beams,  295. 

Deflection  of  rectangular  beams,  294. 

Depth  of  web  at  the  centre  of  main  beam,  150. 

Destructive  effects  produced  by  carriages  on 
roads,  311. 

Devlin's  oil,  297. 

Diagram  of  a  curve  of  sectional  areas,  460. 
Diagram  of  indicator,  265. 
Diameter  of  cylinder,  251. 
Diameter  of  main  centre  journal,  143. 
Diameter  of  plain  part  of  crank  axle,  169. 
Diameter  of  the  outside  bearings  of  the  crank 
axle,  168. 

Diameters  of  wheels  at  their  pitch  circle  to 
contain  a  required  number  of  teeth,  436. 

Dimensions  of  the  several  paa-ts  of  furnaces 
and  boilers,  254. 

Direct  method  to  calculate  the  logarithm  of 
any  number,  346. 

Direct  strain,  278. 

Discharge  by  compound  tubes,  321. 

Discharge  by  different  apertures  from  differ- 
ent heads  of  water,  318. 

Discharge  of  water,  446. 

Discharges  from  orifices,  426. 

Displacement  of  a  ship  when  treated  as  a 
floating  body,  455. 

Displacement  of  ships,  by  vertical  and  hori- 
zontal sections,  460,  500. 

Distance  of  the  piston  from  the  end  of  its 
stroke,  when  the  exhausting  port  is  shut 
and  when  it  is  open,  231. 

Distances,  how  to  measure,  369. 


INDEX. 


571 


Division  by  logarithms,  336. 
Dodecaedron,  89. 

Double  acting  engines,  rods  of,  250. 

Double  position,  44. 

Double  table  of  ordinates,  457. 

Drainage  of  water  through  pipes,  325. 

Dr.  Dalton,  and  his  countryman,  Dr.  Young, 

of  Dublin, 
Drums,  422. 

Drums  in  continuous  circular  motion,  432. 

Dry  or  corn  measure,  8. 

Duodecimals,  27. 

Dutch  sails  of  windmills,  333. 

D.  valves,  233. 

Dynamometer,  used  to  measure  force,  269. 

Eduction  ports,  171. 
Effective  discharge  of  water,  314. 
Effective  heating  surface  of  flue  boilers,  256. 
Effects  of  carriages  on  ordinary  roads,  311. 
Elastic  force  of  steam,  188. 
Elastic  fluids,  205. 
Elliptic  arcs,  69,  70,  71,  72. 
Embankments  and  cuttings,  97. 
Endless  screw,  431. 

Engineering  and  mechanical  materials,  386. 
Engine,  motion  of  steam  in,  206. 
Engine  tender  tank,  92. 
Enlargements  of  pipes,  interruption  of  dis- 
charge by,  321. 
Evolution,  29. 

Evolution  by  logarithms,  339. 
Eye,  diameter  of,  251. 
Eye  of  crank,  136. 

Byo  of  crank,  to  find  the  length  and  breadth 

of  large  and  small,  142. 
Eye  of  round  end  of  studs  of  lever,  143. 
Examples  on  the  velocity  of  wheels,  drums, 

and  pulleys,  438. 
Exhaust  port,  230. 
Expanded  steam,  236. 
Expansion,  237. 

Expansion,  economical  effect  of,  216. 
Experiments  on  the  strength  and  other  pro- 
perties of  cast  iron,  174. 
Explanation  of  characters,  12. 
Extended  theory  of  angular  magnitude,  374. 
Exterior  diameter  of  large  eye,  252. 
Extraction  of  roots  by  logarithms,  339. 

Fall  of  water,  444. 

Feed  pipe,  150. 

Feed  water,  222. 

Felloes  of  wheels,  309. 

Fellowship,  or  partnership,  41. 

Fire-grate,  171,  214. 

Fitzgerald,  264,  269. 

Flange,  91. 

Flat  bar  iron,  407. 

Flat  iron,  400. 

Flexure  by  vertical  pressure,  292. 

Flexure  of  revolving  shafts,  pillars,  &c.,  296. 

Flues,  256. 

Flues,  fires,  and  boilers,  217. 

Fluids,  the  motion  of  elastic,  205. 

Fluids,  to  find  the  specific  gravity  of,  392. 

Fluids,  the  pressure  of,  448. 

Fluid  vein,  contraction  of,  313. 

Foot-valve  passage,  149. 

Force,  267. 

Force,  loss  of,  in  steam  pipes,  221. 


Force  of  steam,  188. 

Forces,  centrifugal  and  centripetal,  178,  450. 

Fore  and  after  bodies  of  immersion,  456,  460. 

Form,  the  strongest,  275. 

Formulas  for  the  strength  of  various  parts 
of  marine  engines,  251. 

Formulas  to  find  the  three  angles  of  a  sphe- 
rical triangle  when  the  three  sides  are 
given,  385. 

Formula,  very  useful,  271. 

Fourth  and  fifth  power  of  numbers,  129. 

Fractions,  common,  15. 

Fractions,  reduction  of,  16,  17,  18,  19. 

Fractions,  addition  of,  20. 

Fractions,  subtraction  of,  21. 

Fractions,  multiplication  of,  21. 

Fractions,  division  of,  21. 

Fractions,  the  rule  of  three  in,  21. 

Fractions,  decimal,  22. 

Fractions,  table  of,  73. 

Fractions,  addition  contracted,  78. 

Fracture,  292. 

Franklin  Institute,  172,  219. 
French  litre,  355. 
French  measures,  5,  6. 
French  metre,  347. 
Friction,  238. 

Friction,  coefficents  of,  300. 

Friction  of  fluids,  325. 

Friction  of  rest  and  of  motion,  267. 

Friction  of  steam  engines  of  difl'erent  modi- 
fications, 302. 

Friction  of  water  against  the  sides  of  pipes,321. 

Friction  of  water-wheels,  windmills,  <tc.,  267. 

Friction,  or  resistance  to  motion,  in  bodies 
rolling  or  rubbing  on  each  other,  297. 

Friction,  laws  of,  298. 

Frustums,  83. 

Frastum  of  spheroid,  87. 

Furnace,  256. 

Furnace  room,  213. 

Gallon,  5. 
Gases,  394. 
Geering,  422. 

General  and  universal  expression,  376. 
General  observations  on  the  steam  engine,259. 
General  trigonometrical  solutions,  365,  369. 
Geometrical  construction,  362. 
Geometrical  construction  of  the  proportion 

of  the  radius  of  a  wheel  to  its  pitch,  440. 
Geometrical  proportion  and  progression,  38. 
Gibs  and  cutter,  140,  253. 
Gibs  and  cutter  through  air  pump  cross-head, 

146,  147. 

Gibs   and   cutter  through   cross-tail  and 

through  butt,  141. 
Gibs  and  cutter,  to  find  the  thickness  and 

breadth  of,  143. 
Girder,  275. 

Girth,  the  mean  in  measuring,  94. 
Glenie,  the  mathematician,  287. 
Globe,  85. 
Grate  surface,  255. 
Gravity,  centre  of,  175,  386. 
Gravity,  specific,  391. 
Gravity,  weight,  mass,  386. 
Gudgeons,  420. 
Gyration,  centre  of,  180,  390. 
Gyration,  the  centre  of  different  figures  and 
bodies,  181. 


r 


572 


INDEX. 


Heads  of  water,  318. 

Heating  surface,  256. 

Heating  surface  of  boilers,  215. 

Heights  and  discharges  of  water,  319. 

Heights  and  distances,  359. 

Height  of  chimneys,  210. 

Height  of  metacentre,  470,  483. 

Hewn  and  sawed  timber,  95. 

Hexagon,  heptagon,  48. 

High  pressure  and  condensing  engines,  234. 

Hollow  shafts,  to  find  the  strength  of,  284. 

Horizontal  distance  of  centre  of  radius  bar, 

246,  247. 
Horse  power,  240. 

Horse  power  of  an  engine,  dimensions  made 
to  depend  upon  the  nominal  horse  power 
of  an  engine,  147. 

Horse  power  of  pumping  engines,  447. 

Horse  power,  tables  of,  243,  244. 

Hot  blast,  174. 

Hot  liquor  pumps,  446. 

Hydraulic  pressure  working  machinery,  330. 
Hydraulics,  267,  312. 
Hydrogen,  weight  of,  356. 
Hydrostatic  press,  448. 
Hyperboloid,  88. 

Hyperbolic  logarithms,  130  to  133. 
Hj'perbolic  logarithms,  how  to  calculate,  353. 
Hypothenuse  of  a  spherical  triangle,  to  find, 
378. 

Hypothenuse,  47. 

ICOSAEDRON,  89. 

Immersed  portions  of  a  ship,  to  calculate, 
456. 

Immersion  and  emersion,  493. 
Impact,  449. 

Impinging  of  elastic  and  inelastic  bodies, 
452. 

Inaccessible  distances,  372. 

Inches  in  a  solid  foot,  96. 

Inclined  plane,  428,  429,  430. 

Inclination  of  the  traces  of  ordinary  car- 
riages, 311. 

Inclinations,  discharge  of  a  6-inch  pipe  at 
several,  326. 

Increase  of  efBciency  arising  from  working 
steam  expansively,  262. 

Index  of  logarithms,  334. 

Indicator,  264,  266. 

Indicator,  the  amount  of  the  effective  power 

of  steam  by,  266. 
Induction  ports,  171. 
Inelastic  bodies,  449. 

Influence  of  pressure,  velocity,  width  of  fel- 
loes, and  diameter  of  wheels,  309. 
Initial  plane,  456,  480,  500. 
Initial  velocity  with  a  free  descent,  388. 
Injection  pipe,  150. 
Inside  discharging  turbine,  330. 
Integer,  10. 

Integers,  to  find  the  square  root  of,  125. 
Interest,  simple,  42. 
Interest,  compound,  43. 
Involution,  28. 

Involution,  or  the  raising  of  powers  by  loga- 
rithms, 338. 
Irregular  polygons,  54. 
Iron,  forged  and  wrought,  272. 
Iron  plates,  403. 
Iron,  properties  of,  175. 


Iron,  strength  of,  173. 

Iron,  taper  and  parallel,  angle  and  T,  rail- 
way and  sash,  408,  411. 

Jet,  specific  gravity  of,  394. 
J ournal  of  cross-head,  to  find  diameter  of,139. 
Journal  of  cross-head,  to  find  the  length 
of,  139. 

Journal,  the  mean  centre,  to  find  the  diameter 

of,  143. 
Journal,  strain  of,  252. 
Journals  for  air-pump  cross-head,  145. 
Journals  for  shafts  of  various  diameters,  287. 
Julian  year,  357. 

Juste  Byrge,  the  inventor  of  logarithms,  133. 

Kane,  Fitzgerald,  269. 
Keel  and  keelson,  433  to  500. 
Kilometre,  5. 
Kilogramme,  6. 
Knots,  nodes,  &c.,  412. 

Lathe  spindle  wheel,  435. 

Laying  off  of  angles  by  compasses  only,  384. 

Leg  of  a  spherical  triangle,  to  find,  377. 

Length  of  crank  pin  of  locomotive,  170. 

Length  of  paddle-shaft  journal,  138. 

Length  of  stroke,  227,  251. 

Lengths  that  may  be  given  to  stroke  of  the 

valve,  229. 
Lengths  of  circular  arcs,  68. 
Lever,  426. 

Light  displacement,  459. 

Line  of  direction,  390. 

Link  next  the  radius  bar,  242. 

Living  forces,  or  the  principle  of  vis  viva,270. 

Load  immersion,  456,  457. 

Load-water  line,  456,  470. 

Locomotive  engine,  parts  of  the  cylinder,  171. 

Locomotive  engine,  diameter  of  the  outside 

bearings  for,  163. 
Locomotive  engine,  dimensions  of  several 

moving  parts,  171. 
Locomotive  engine,  dimensions  of  several 

pipes,  171. 

Locomotive  engine,  parts  of  the  boiler,  171. 
Locomotive  engine,  tender  tank,  92. 
Locomotive  and  other  engines,  233. 
Logarithmic  calculations,  376. 
Logarithmic  calculations  of  the  force  of 

steam,  190  to  193. 
Logarithmic  sines,  tangents,  and  secants  for 

every  minute  in  the  quadrant,  540,  576. 
Logarithms  applied  to  angular  magnitudes, 

359. 

Logarithms,  hyperbolic,  130. 

Logarithms  of  the  natural  numbers  from  1 

to  100000  by  the  help  of  differences,  503 

to  540. 

Logarithms,  the  application  of,  334. 
Long  measure,  7. 

Longitudinal  distance  of  the  centre  of  gravity 

of  displacement,  470,  500. 
Loss  of  force  by  the  decrease  of  temperature 

in  the  steam  pipes,  221. 
Low  pressure  engines,  243. 
Lunes,  54. 

IMachinery,  elements  of,  425. 
Waehinerv  worked  by  hydraulic  pressure, 
330. 


INDEX. 


573 


Major  and  minor  diameters  of  cross-head, 
253. 

Main  beam  at  centre,  249. 
Malleable  iron,  396. 
]\larble,  288. 
Marine  boilers,  217. 
Mass,  267. 

Mass,  gravity,  and  weight,  386. 
Mass  of  a  body,  to  find,  when  the  weight  is 
given,  389. 

Materials  employed  in  the  construction  of 

machines,  267. 
Materials,  their  properties,  torsion,  deflexion, 

&c.,  267. 
Ma.ximum  accelerating  force,  421. 
Maximum  velocity  and   power   of  water 

wheels,  443. 
Measures  and  weights,  5. 
Measurement  of  angular  magnitudes,  374. 
Measurement  of  angles  by  compasses  only, 

382. 

Mechanical  effect,  417. 

Mechanical  powers,  422. 

Mechanical  power  of  steam,  261. 

Mensuration  of  solids,  79. 

Mensuration  of  timber,  93. 

Mensuration  of  superficies,  45. 

Mercury,  density  of,  350. 

Mercury,  to  calculate  the  force  of  steam  in 

inches  of,  201. 
Method  to  calculate  the  logarithm  of  any 

given  number,  340. 
Metacentre,  453,  466,  483. 
Metre,  6. 

Midship,  or  greatest  transverse  section,  460, 

488. 
Millboard,  405. 
Millstones,  445. 
Millstones,  strength  of,  451. 
Modulus  of  elasticity,  278. 
Modulus  of  logarithms,  343. 
Modulus  of  torsion  and  of  rupture,  279. 
Moment  of  inertia,  412. 
Motion  of  elastic  fluids,  205. 
Motion  of  steam  in  an  engine,  206. 
Multiplication  of  decimals,  23. 
Multiplication  of  fractions,  21. 
Multiplication  by  logarithms,  335. 
Musical  proportion,  40. 

Natural  sines,  cosines,  tangents,  cotangents, 

secants,  and  cosecants,  to  every  degree  of 

the  quadrant,  411. 
Naval  architecture,  453. 
New  method  of  multiplication,  342. 
Nitrogen,  weight  of,  356. 
Nominal  horse  power,  tables  of,  for  high  and 

low  pressure  engines,  243,  244. 
Notation  and  numeration,  10. 
Notation,  trigonometrical,  369. 
Number  corresponding  to  a  given  logarithm, 

351. 

Number  of  teeth,  or  the  pitch  of  small 

wheels,  435. 
Numbers,  fourth  and  fifth  powers  of,  129. 
Numbers,  logarithms  of,  640,  756. 
Numbers,  reciprocals  of,  73  to  78. 
Numbers,  squares,  cubes,  &c.,  of,  100  to  116. 
Numeral  solution  of  the  several  cases  of 

trigonometry,  361. 
Nuts  and  bolts,  406. 


Oak,  Dantzic,  280. 

Obelisk,  to  find  the  height  of,  371. 

Oblique  triangles,  368. 

Observatory  at  Paris  ff  =  9-80896  metres,346. 
O'Byrne's  turbine  tables,  331. 
Octagon,  48. 
Octaedron,  89. 
O'Neill's  experiments,  447. 
O'Neill's  rules  employed  in  the  art  of  ship- 
building, 454. 
Opium,  specific  gravity  of,  394. 
Orders  of  lever,  426. 

Ordinates  employed  in  the  art  of  ship-build- 
ing, 455,  456,  458,  500. 
Orifices  and  tubes,  discharge  of  water  by,  312. 
Orifices,  rectangular,  314. 
Oscillation,  centre  of,  187,  391. 
Outside  bearings  of  crank  axle,  168. 
Outside  discharging  turbines,  331. 
Overshot  wheels,  329. 

Overshot  wheels,  maximum  velocity  of,  443. 
Ox-hide,  299. 
Oxygen,  214,  356. 

PADDLE-shaft  journal,  137,  251. 
Paraboloid,  88. 
Parabolic  conoid,  88. 
Parallel  angle  iron,  409. 
Parallel  motion,  242  to  246. 
Parallelogram  of  forces,  422. 
Parallelopipedon,  80. 
Partnership,  41. 

Partial  contraction  of  the  fluid  vein,  316. 

Passages,  area  of  steam,  220. 

Peclet's  expression  for  the  velocity  of  smoke 

in  chimneys,  213. 
Pendulums,  183,  391. 
Pendulum,  conical,  184. 
Pendulums,  vibrating  seconds  at  the  level  of 

the  sea  in  various  latitudes,  393. 
Percussion,  centre  of,  391. 
Periodic  time,  179. 

Permanent  weight  supported  by  beams,  284. 
Permutations  and  combinations,  44. 
Pillars,  strength  of,  293. 
Pinions  and  wheels  in  continuous  circular 

motion,  432. 
Pipes,  discharge  and  drainage  of  wnter 

through,  321,  322,  325. 
Pipes  of  cast  iron,  395. 
Pipes  for  marine  engines,  149. 
Piston,  251. 

Piston  of  steam  engine,  414. 

Piston  rod,  140,  171,  253. 

Piston  rod  of  air-pump,  146. 

Pitch  circle,  436. 

Pitch  of  teeth,  441. 

Pitch  of  wheels,  435,  439. 

Plane  triangles,  solution  of,  364,  365. 

Plane  trigonometry,  359. 

Planks,  deals,  94. 

Polygons,  47,  48. 

Polygons,  irregular,  54. 

Port,  upper  and  lower,  229. 

Position,  double,  44. 

Position,  single,  43. 

Pound,  5. 

Power,  actual  and  nominal,  241. 
Power  and  properties  of  steam,  261. 
Power  that  a  cast-iron  wheel  is  capable  of 
transmitting,  442. 


574 


INDEX. 


Power  of  shafts,  294. 

Practical  application  of  the  mechanical 

powers,  425. 
Practical  limit  to  expansion,  261. 
Practical  observations  on  steam  engines,  260. 
Principle  of  virtual  velocities,  423. 
Prism,  80. 
Prismoid,  85. 
Properties  of  bodies,  401. 
Proportional  dimensions  of  nuts  and  bolts, 

406. 
Proportion,  14. 
Proportion,  musical,  40. 
Proportion  and  progression,  arithmetical,  35 

to  38. 

Proportion  and  progression,  geometrical,  38 
to  40. 

Proportion,  or  the  rule  of  three  by  loga- 
rithms, 338. 
Proportion  of  wheels  for  screw-cutting,  433. 
Proportions  of  boilers,  grates,  Ac,  213. 
Proportions  of  the  lengths  of  circular  arcs,  68. 
Proportions  of  undershot  wheels,  328. 
Pulleys,  422,  427. 
Pump  and  pumping  engines,  446. 
Pumping  engines,  422. 
Pyramid,  82. 
Pyrometer,  63. 

Quadrant,  359. 

Quadrant,  log.  sines,  cosines,  &c.,  for  every 
minute  in,  540,  576. 

Quadrant,  natural  sines  and  cosines  for 
every  degree  of,  411. 

Quadrant,  to  take  angles  with,  370. 

Quantities,  known  and  unknown,  134. 

Quantity  of  water  that  flows  through  a  cir- 
cular orifice,  313,  319. 

Quiescence,  friction  of,  299. 

Radius  bar,  242. 

Radius  bar,  length  of,  corrected,  248. 

Radius  of  the  earth  at  Philadelphia,  356. 

Radius  of  gyration,  412. 

Radius,  length  of,  in  degrees,  357. 

RaUs,  temporary,  411. 

Railway  carriage.  268. 

Railway  iron,  410. 

Raising  of  powers  by  logarithms,  338. 
Reciprocals  of  numbers,  73  to  78. 
Recoil,  449. 

Rectangle,  rhombus,  rhomboides,   to  find 

the  areas  of,  45,  46. 
Reduction  of  fractions,  16,  17,  to  19,  20. 
Regnault's  experiments  on  oxygen,  &e.,  356. 
Regular  bodies,  90. 

Relative  capacities  of  the  two  bodies  under 
the  same  displacement,  456,  470. 

Relative  strength  of  materials  to  resist  tor- 
sion, 294. 

Revolving  shaft,  250. 

Riga  fir,  290. 

Right-angled  spherical  triangles,  374. 

Ring,  circular,  to  find  the  area  of,  53. 

Ring,  cylindrical,  90. 

Roads,  traction  of  carriages  on,  307. 

Rolled  iron,  395. 

Roman  notation,  11. 

Rope,  strength  of,  282. 

Ropes,  bands,  &c.,  267. 

Ropes,  blocks,  pulleys,  428. 


Ropes,  stiffness  of,  resistance  of,  to  bendin 
302. 

Ropes,  tarred  and  dry,  304,  306. 

Rotative  engines,  260. 

Rotation,  moment  of,  414. 

Rotation  of  a  body  about  a  fixed  axis,  416. 

Rotations  of  miUstones,  452. 

Round  and  rectangular  bars,  strength  of,  2S1. 

Round  bar-iron,  4U3. 

Round  steel  and  brass,  408. 

Rules  for  pumping  engines,  448. 

Rule  of  three,  13. 

Rule  of  three  by  logarithms,  338. 

Rule  of  three  in  fractions,  21. 

Rupture,  272. 

Safety  valves,  149,  150,  224. 
Sails  of  windmills,  332. 
Sash  iron,  410. 

Scales  of  chords,  how  to  construct,  360. 

Scale  of  displacement,  465. 

Scantling,  95.  , 

Screw  cutting  by  lathe,  433. 

Screw,  power  of,  430. 

Screw,  to  cut,  434. 

Sectional  area  measured,  456. 

Segments  of  circles,  64  to  67. 

Shelves,  cords,  blocks,  428. 

Ship-budding  and  naval  architecture,  453. 

Sidereal  day,  9. 

Side  lever,  to  find  the  depth  across  the  centre 

of,  144. 
Side  rod,  246,  254. 
Side  rod  of  air-pump,  146. 
Sines,  cosines,  &c.,  411. 
Sines,  tangents  and  secants,  359. 
Singular  phenomena,  237. 
Sleigh,  268. 
Slide  valve,  225. 

Slide  valve,  a  cursory  examination  of,  232. 
Slopes  li  to  1,  2  to  1,  and  1  to  1,  97. 
Sluice  board,  316. 

Smoke  and  heated  air  in  chimneys,  202. 

Solid  inches  in  a  solid  foot,  96. 

Solids,  mensuration  of,  79. 

Space  described  by  a  body  during  a  free  de- 
scent in  vacuo,  388. 

Specific  gravity,  386,  391. 

Sphere,  85. 

Spheres,  397  to  400. 

Spheroid,  86,  87,  88. 

Spherical  trigonometry,  373. 

Spheroidal  condition  of  water  in  boilers,  236. 

Spindle  and  screw  wheels,  434. 

Square,  to  find  the  area  of,  45. 

Square  and  sheet  iron,  402. 

Squares  and  square  roots  of  numbers,  100 
to  116. 

Square  root,  30. 

Square  root  of  fractions  and  mixed  numbers, 
31. 

Square  measure,  6. 

Stability,  459,  499. 

Stars,  apparent  motion  of,  353. 

Statical  moment,  417. 

Steam  engine,  135. 

Steam  dome,  171. 

Steam  passages.  220, 

Steam  pipes,  loss  of  force  in,  222. 

Steam  port,  147,  148. 

Steam  room,  259. 


INDEX. 


575 


Steam,  elastic  force  of,  188  to  202. 
Steam,  temperature  of,  pressure  of,  172. 
Steam,  volume  of,  202  to  206. 
Steam,  weight  of,  204. 
Steel,  408. 

Stiffness  of  a  ressel  under  canvas,  485. 
Stiffness  of  ropes,  302,  306. 
Stowage,  503. 

Stowing  the  hold  of  a  vessel,  453,  456. 
Strap  at  cutter,  141. 

Strap,  mean  thickness  of,  at  and  before  cut- 
ter, 143. 

Strength  of  bodies,  282. 

Strength  of  boilers,  218. 

Strength  of  materials,  173,  271. 

Strength  of  rods  when  the  strain  is  wholly 
tensile,  250. 

Strength  of  the  teeth  of  cast  iron  wheels,  437. 

Studs  of  lever,  14.3. 

Stud-wheel  and  pinion,  434. 

Subtraction  of  decimals,  23. 

Subtraction  of  fractions,  21. 

Table  by  which  to  determine  the  number  of 
teeth  or  pitch  of  small  wheels,  435. 

Table  containing  the  circumferences,  squares, 
cubes,  and  areas  of  circles,  from  1  to  100, 
advancing  by  a  tenth,  57,  68,  59,  60  to 
63. 

Table  containing  the  weight  of  columns  of 
water,  each  one  foot  in  length,  in  pounds 
avoirdupois,  401. 

Table  containing  the  weight  of  square  bar 
*  iron,  402. 

Table  containing  the  surface  and  solidity  of 
spheres,  together  with  the  edge  of  equal 
cubes,  the  length  of  equal  cylinders,  and 
weight  of  water  in  avoirdupois  pounds, 
397. 

Table  containing  the  weight  of  flat  bar  iron, 
400. 

Table  containing  the  specific  gravities  and 
other  properties  of  bodies;  water  the  stand- 
ard of  comparison,  401. 

Table  containing  the  weight  of  round  bar 
iron,  403. 

Table  containing  the  weights  of  cast  iron 
pipes,  404. 

Table  containing  the  weight  of  solid  cylin- 
ders of  cast  iron,  404. 

Table  containing  the  weight  of  a  square  foot 
of  copper  and  lead,  405. 

Table  for  finding  the  weight  of  malleable 
iron,  copper,  and  lead,  405. 

Table  for  finding  the  radius  of  a  wheel  when 
the  pitch  Is  given,  or  the  pitch  when  the  ra- 
dius is  given,  for  any  number  of  teeth,  439. 

Table  for  the  general  construction  of  tooth 
wheels,  442. 

Table  for  breast  wheels,  329. 

Table  of  polygons,  48. 

Table  of  decimal  approximations  for  facili- 
tating calculations,  55. 

Table  of  decimal  equivalents,  56. 

Table  of  the  areas  of  the  segments  and  zones 
of  a  circle  of  which  the  diameter  is  unity, 
64,  65,  66,  67. 

Table  of  the  proportions  of  the  lengths  of 
semi-elliptic  arcs,  69,  70,  72. 

Table  of  tiat  or  board  measure,  93. 

Table  of  solid  timber  measure,  94. 


Table  of  reciprocals  of  numbers,  or  of  the 
decimal  fractions  corresponding  to  com- 
mon fractions,  71  to  77,  78. 

Table  of  weights  and  values  in  decimal 
parts,  79. 

Table  of  regular  bodies,  90. 

Table  of  the  cohesive  power  of  bodies,  175. 

Table  of  hyperbolic  logarithms,  130  to  133. 

Table  of  the  pressure  of  steam,  in  inches  of 
mercury  at  different  temperatures,  172. 

Table  of  the  temperature  of  steam  at  differ- 
ent pressures,  in  atmospheres,  172. 

Table  of  the  expansion  of  air  by  heat,  173. 

Table  of  the  strength  of  iron,  173. 

Table  of  the  superficial  and  solid  content  of 
spheres,  96. 

Table  of  solid  inches  in  a  solid  foot,  96. 

Table  of  squares,  cubes,  square  and  cube 
roots,  of  numbers,  100,  101,  116,  125. 

Table  of  cover  on  the  exhausting  side  of  the 
valve  in  parts  of  the  stroke  and  distance 
of  piston  from  the  end  of  its  stroke,  231. 

Table  of  the  proportions  of  the  lengths  of 
circular  arcs,  68. 

Table  of  the  fourth  and  fifth  power  of  num- 
bers, 129. 

Table  of  the  properties  of  different  boil- 
ers, 215. 

Table  of  the  economical  effects  of  expan- 
sion, 216. 

Table  of  the  comparative  evaporative  power 

of  different  kinds  of  coal,  218. 
Table  of  the  cohesive  strength  of  iron  boiler 

plate  at  different  temperatures,  219. 
Table  of  diminution  of  strength  of  copper 

boilers,  219. 
Table  of  expanded  steam,  239. 
Table  of  the  proportionate  length  of  bearings, 

or  journals  for  shafts  of  various  diameters, 

287. 

Table  of  tenacities,  resistances  to  compres- 
sion and  other  properties  of  materials, 
288. 

Table  of  the  strength  of  ropes  and  chains, 
288. 

Table  of  the  strength  of  alloys,  289. 
Table  of  data  of  timber,  289. 
Table  of  the  properties  of  steam,  261. 
Table  of  the  mechanical  properties  of  steam, 
263. 

Table  of  the  cohesive  strength  of  bodies,  281. 

Table  of  the  strength  of  common  bodies,  283. 

Table  of  torsion  and  twisting  of  common  ma- 
terials, 286. 

Table  of  the  length  of  circular  arcs,  radius 
being  unity,  63. 

Table  of  experiments  on  iron  boiler  plate  at 
high  temperature,  220. 

Table  of  the  absolute  weight  of  cylindrical 
columns,  274. 

Table  of  flanges  of  girders,  276. 

Table  of  mean  pressure  of  steam  at  different 
densities  and  rates  of  expansion,  239. 

Table  of  nominal  horse  power  of  high  pres- 
sure engines,  244. 

Table  of  nominal  horse  power  of  low  pres- 
sure engines,  243. 

Table  of  dimensions  of  cylindrical  columns 
of  cast  iron  to  sustain  a  given  load  with 
safety,  293. 

Table  of  strength  of  columns,  294. 


576 


INDEX. 


Table  of  compnrntive  torsion,  294. 

Table  of  the  depths  of  square  beams  to  sup- 
port from  1  ewt.  to  14  tons,  295,  296. 

Table  of  the  results  of  experiments  on  fric- 
tions, with  unguents  interposed,  29'J,  300. 

Table  of  the  results  of  experiments  on  the 
gudgeons  or  axle-ends  in  motion  upon  their 
bearings,  301. 

Table  of  friction,  continued  to  abrasion,  301. 

Table  of  friction  of  steam  engines  of  differ- 
ent modifications,  302. 

Table  of  tarred  ropes,  303. 

Table  of  white  ropes,  305. 

Table  of  dry  and  tarred  ropes,  306. 

Table  of  the  pressure  and  traction  of  car- 
riages, 308. 

Table  of  traction  of  wheels,  309. 

Table  of  the  ratio  of  traction  to  the  load, 
310. 

Table  of  the  coefficients  of  the  efflux  through 
rectangular  orifices  in  a  thin  vertical  plate, 
315. 

Table  of  the  coefficients  of  efflux,  315. 

Table  of  comparison  of  the  theoretical  witb 
the  real  discharges  from  an  orifice,  317. 

Tabic  of  discharge  of  tubes  of  different  en- 
largements, 322. 

Table  of  the  comparison  of  discharge  by  pipes 
of  different  lengths,  323. 

Table  of  the  comparison  of  discharge  by  ad- 
ditional tubes,  323. 

Table  of  the  friction  of  fluids,  325. 

Table  of  discharges  of  a  6-inch  pipe  at  seve- 
ral inclinations,  326. 

Table  of  the  velocity  of  windmill  sails,  333. 

Table  of  outside  discharging  turbine,  331. 

Table  of  inward  discharging  turbines,  332. 

Table  of  peculiar  logarithms,  3-10. 

Table  of  useful  logarithms,  345. 

Table  of  the  specific  gravity  of  various  sub- 
stances, 394. 

Table  of  the  weight  of  a  foot  in  length  of  flat 
and  rolled  iron,  395. 

Table  of  the  weight  of  cast  iron  pipes,  395. 

Table  of  the  weight  of  one  foot  in  length  of 
malleable  iron,  396. 

Table  of  comparison,  396. 

Table  of  the  weight  of  a  square  foot  of  sheet 
iron,  402. 

Table  of  the  weight  of  a  square  foot  of  boiler 
plate  from  J  of  an  inch  to  1  inch  thick,  403. 

Table  of  the  weights  of  cast  iron  plates,  403. 

Table  of  the  weight  of  mill-board,  405. 

Table  of  the  weiglit  of  wrought  iron  bars,  406. 

Table  of  the  proportional  dimensions  of  nuts 
and  bolts,  406. 

Table  of  the  specific  gravity  of  water  at  dif- 
ferent temperatures,  406. 

Table  of  the  weight  of  cast  iron  balls,  407. 

Table  of  the  weight  of  flat  bar  iron,  407. 

Table  of  the  weight  of  square  and  round 
brass,  408. 

Table  of  taper  T  iron,  410. 

Table  of  sash  iron,  410. 

Table  of  rails  of  equal  top  and  bottom,  410. 

Table  of  temporary  rails,  411. 

Table  of  natural  sines,  cosines,  tangents,  co- 
tangents, secants,  and  cosecants,  to  every 
degree  of  the  quadrant,  411. 

Table  of  inclined  planes,  showing  the  ascent 
or  descent  the  yard,  430. 


Table  of  the  weight  of  round  steel,  408. 
Table  of  parallel  angle  iron  of  equal  sides,  408. 
Table  of  parallel  angle  iron  of  unequal  sides, 
409. 

Table  of  taper  angle  iron  of  equal  sides,  409. 
Table  of  parallel  T  iron  of  unequal  width  and 
depth,  409. 

Table  of  change  wheels  for  screw-cutting, 
435. 

Table  of  the  diameters  of  wheels  at  their 
pitch  circle,  to  contain  a  required  number 
of  teeth,  436. 

Table  of  the  angle  of  windmill  sails,  445. 

Table  of  the  logarithms  of  the  natural  num- 
bers, from  1  to  100000,  by  the  help  of  dif- 
ferences, 602  to  640. 

Table  of  log.  sines,  cosines,  tangents,  cotan- 
gents, secants  and  cosecants,  for  every  de- 
gree and  minute  in  the  quadrant,  540  to 
676. 

Table  of  the  strength  of  the  teeth  of  cast  iron 
wheels  at  a  given  velocity,  437. 

Table  of  approved  proportions  for  wheels 
with  flat  arms,  441. 

Table  showing  the  cover  required  on  the 
steam  side  of  the  valve  to  cut  the  steam  off 
at  any  part  of  the  stroke,  228. 

Table  showing  the  cover  required,  227. 

Table  showing  the  resistance  opposed  to 
the  motion  of  carriages  on  different  incli- 
nations of  ascending  or  descending  planes, 
429. 

Table  showing  the  number  of  linear  feet  of 
scantling  of  various  dimensions  which  are 
equal  to  a  cubic  foot,  95. 

Table  showing  the  weight  or  pressure  a  beam 
of  cast  iron  wiD  sustain  without  destroying 
its  elastic  force,  292. 

Table  showing  the  circumference  of  rope 
equal  to  a  chain,  282. 

Table  to  correct  parallel  motion  links,  248. 

Table  of  parallel  T  iron  of  equal  depth  and 
width,  410. 

Tables  of  cuttings  and  embankments,  slopes, 
1  to  1  ;  14  to  1 ;  and  2  to  1,  97. 

Tables  of  the  heights  corresponding  to  differ- 
ent velocities,  389. 

Tables  of  the  mechanical  properties  of  the 
materials  most  commonly  employed  in  the 
construction  of  machines  and  framings, 
280. 

Tangents,  360. 

Tangents  and  secants,  to  compute,  362. 
Taper  angle  iron,  410. 
Teeth  of  wheels  in  continuous  circular  motion, 
432. 

Teeth  of  wheels,  422,  436. 

Temperature  of  steam,  172. 

Temperature  and  elastic  force  of  steam,  188. 

Tension  of  chain-bridge,  414. 

Tetraedron,  89. 

Threshing  machines,  445. 

Throttling  the  steam,  234. 

Timber  measure,  93. 

Timber,  to  measure  round,  95. 

Time,  7. 

Tonnage  of  ships,  461. 
Torsion,  279. 

Torsion  and  twisting,  286. 
Traction  of  carriages,  307. 
Transverse  strength  of  bodies,  282. 


» 


INDEX. 


577 


Transverse  strain,  278. 
Transverse  strain,  time  weight,  273. 
Trapezium,  47. 
Trapezoid,  47. 

Triangle,  to  find  the  area  of,  46,  47. 

Trigonometry,  359. 

Trigonometrj',  spherical,  373. 

Troy  weight,  7. 

Trussed  beams,  291. 

Tubes,  discbarge  of  water  through,  312. 

Tubular  boilers,  257. 

Turbine  water-wheels,  330. 

Ultimate  pressure  of  expanded  steam,  236. 

Undecagon,  47. 

Undershot  wheels,  327,  443. 

Unguents,  299. 

Ungulas,  cylindrical,  81. 

Ungulas,  conical,  83,  84. 

Unit  of  length,  5. 

Unit  of  weight,  5. 

Unit  of  dry  capacity,  5. 

Units  of  liquids,  5. 

Units  of  work,  269,  297,  414,  4lo. 

Universal  pitch  table,  442. 

Upper  steam  port,  229. 

Useful  formula,  271. 

Use  of  the  table  of  squares,  cubes,  &c.,  127. 

Vacuum,  perfect  one,  235. 
Vacuum  below  the  piston,  251. 
Vacuo,  bodies  falling  freely  in,  388. 
Valves,  different  arrangements  of,  233. 
Valve,  length  of  stroke  of,  in  inches,  228. 
Valve  shaft,  147. 
Valve,  safety,  224. 
Valve,  slide,  225. 
Valve  spindle,  171. 
Vapour  in  the  cylinder,  229. 
Vein,  contraction  of  iluid,  330. 
Velocity,  force,  and  work  done,  267. 
Velocity  of  steam  rushing  into  a  vacuum,  207. 
Velocity  of  smoke  in  chimneys,  209,  213. 
Velocity  of  piston  of  steam  engine,  266. 
Velocity  of  threshing  machines,  millstones, 

boring,  &c.,  445. 
Velocity  of  wheels  on  ordinary  roads,  307. 
Venhiri,  experiments  of,  on  the  discharge  of 

fluids,  421. 
Versed  sine,  tabular,  52. 
Versed  sine  of  parallel  motion,  244. 
Versed  sine,  359. 


Vertical  sectional  areas,  454. 
Virtual  velocities,  424. 

Vis  viva,  principle  of,  calculations  on,  276, 
388. 

Volume  of  a  ship  immersed,  456. 
Volume  of  steam  in  a  cubic  foot  of  water, 
202,  205. 

Water,  modulus  of  elasticity  of,  190. 
Water  level,  214. 
Water,  feed  and  condensing,  223. 
Water,  spheroidal  condition  of,  in  boilers,236. 
Water  in  boiler,  and  water  level,  358. 
Water,  discharge  of,  through  different  orifi- 
ces, 312,  318. 
Water  wheels,  327. 

Water  wheels,  maximum  velocity  of,  443. 
Web  of  crank  at  paddle  shaft  centre,  136. 
Web  of  cross-head  at  middle,  139. 
Web  of  crank  at  pin  centre,  142. 
Web  at  paddle  centre,  252. 
Web  of  cross-head  at  journal,  140. 
Web  of  air-pump  cross-head,  145. 
Wedge,  85. 

Wedge  and  screw,  430. 

Weights  and  measures,  5. 

AVeights,  values  of,  in  decimal  parts,  79. 

Weight,  mass,  gravity,  386. 

Weirs,  and  rectangular  apertures,  314,  323. 

Wheel  and  axle,  417. 

AVheel  and  pinion,  427. 

Wheels,  drums,  pulleys,  438. 

Windmills,  332. 

Wine  measure,  8. 

Woods,  280. 

Woods,  specific  gravity,  394. 
Work  done,  weight,  267. 
Wrought  iron  bars,  406. 

Yard,  5. 

Yacht,  admeasurement  of,  469  470. 
Yarns  of  ropes,  303. 
Yellow  brass,  281. 
Yew,  280. 

Zinc,  280. 
Zinc,  sheet,  288. 
Zone,  spherical,  86. 

Zone,  to  find  the  area  of  a  circular,  53. 
Zones  of  circles,  to  find  the  areas  of,  64,  65, 
66. 


PUBLICATIONS 

OF 


HENRY    CARET   B  A  I  R  D, 


SUCCESSOR  TO  E.  L.  CARET, 


South-east  corner  of  Market  and  Fifth  Streets,  Philadelphia. 


SCIENTIEIC  AND  PRACTICAL. 


THE  PRACTICAL  MODEL  CALCULATOR, 

For  the  Engineer,  Machinist,  Manufacturer  of  Engine  Work, 

Naval  Architect,  Miner,  and  Millwright.  By  Oliver  Byrne,  Compiler  and  Editor 
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felling  of  a  tree,  up  to  the  most  elaborate  production  of  ornamental  architecture.  It  is  seientitic,  without 
being  obscure  and  unintelligible,  and  every  house-carpenter,  master,  journeyman,  or  apprentice,  should 
have  a  copy  at  hand  always. — Evening  Bulletin. 

Complete  on  the  subjects  of  which  it  treats.   A  most  useful  practical  work. — Baltimore  American, 

It  must  be  of  great  practical  utility. — Savannah  Republican. 

To  whatever  branch  of  the  art  of  building  the  reader  may  belong,  he  will  find  in  this  something  valuable 
and  calculated  to  assist  his  progress. — Farmer  and  Mechanic. 

This  is  a  valuable  little  volume,  designed  to  assist  the  student  in  the  acquisition  of  elementary  knowledge, 
and  will  be  found  highly  advantageous  to  every  young  man  who  has  devoted  himself  to  the  interesting 
pursuits  of  which  it  treats. — Virginia  Herald. 


A  TREATISE  ON  A  BOX  OF  INSTRUMENTS, 

And  the  Slide  Rule,  with  the  Theory  of  Trigonometry  and 

Logarithms,  including  Practical  Geometry,  Surveying,  Measuring  of  Timber,  Cask 
and  Malt  Gauging,  Heights  and  Distances.  By  Thomas  Kentish.  In  One 
Volume,  12mo. 


PUBLICATIONS  OF  HENRY  CAREY  BAIitD. 


5 


THE  CABINET-MAKER  AND  UPHOLSTERER'S  COMPANION: 

Comprising  the  Rudiments  and  Principles  of  Cabinet-making 

and  Upholstery,  with  familiar  InstructioBS,  illustrated  by  Examples,  for  attaining 
a  proficiency  in  the  Art  of  Drawing,  as  applicable  to  Cabinet-Work  ;  the  processes 
of  Veneering,  Inlaying,  and  Buhl  Work  ;  the  art  of  Dyeing  and  Staining  AVood, 
Bone,  Tortoise-shell,  &c.  Directions  for  Lackering,  Japanning,  and  Varnishing ; 
to  make  French  Polish ;  to  prepare  the  best  Glues,  Cements,  and  Compositions, 
and  a  number  of  Receipts  particularly  useful  for  Workmen  generally,  with  Ex- 
planatory and  Illustrative  Engravings.  By  J.  Stokes.  In  One  Volume,  12mo, 
with  Illustrations  75  cts. 

A  large  amount  of  practical  information,  of  great  service  to  all  concerned  in  those  branches  of  business. 
— Ohio  State  Journal. 


PROPELLERS  AND  STEAM  NAVIGATION: 

With  Biographical  Sketches  of  Early  Inventors.    By  Robert 

Macfarlane,  C.  E.,  Editor  of  the  "  Scientific  American."    In  One  Volume,  12mo. 

Illustrated  by  over  Eighty  Wood  Engravings  75  cts. 

The  object  of  this  "  History  of  Propellers  and  Steam  Navigation"  is  twofold.  One  is  the  arrangement 
an'  description  of  many  devices  which  have  been  invented  to  propel  vessels,  in  order  to  prevent  many  in- 
gc^n.ous  men  from  wasting  their  time,  talents,  and  money  on  such  projects.  The  immense  amount  of  time, 
study,  and  money  thrown  away  on  such  contrivances  is  beyond  calculation.  In  this  respect,  it  is  hoped 
that  it  will  be  the  means  of  doing  some  good. — Preface. 


TABLES  OF  LOGARITHMS  FOR  ENGINEERS  AND  MACHINISTS: 

Containing  the  Logarithms  of  the  Natural  Numbers,  from  1  to 

100000,  by  the  help  of  Proportional  Diiferences.  And  Logarithmic  Sines,  Co- 
sines, Tangents,  Co-tangents,  Secants,  and  Co-secants,  for  every  Degree  and  Mi- 
nute in  the  Quadrant.  To  which  are  added.  Differences  for  every  100  Seconds.  By 
Oliveb  Byrne,  Civil,  Military,  and  Mechanical  Engineer.   In  One  Vol.  8vo.  cl....  $1 


THE  FRUIT,  FLOWER,  AND  KITCHEN  GARDEN. 

By  Patrick  Neill,  L.  L.  D.,  F.  R.  S.  E.,  Secretary  to  the 

Royal  Caledonian  Horticultural  Society.    Adapted  to  the  United  States,  from  the 

Fourth  Edition,  revised  and  improved  by  the  Author.    Illustrated  by  fifty  Wood 

Engravings  of  Hothouses,  &c.  &c.    In  One  Volume,  12mo  .$1.25 

This  volume  supplies  a  desideratum  much  felt,  and  gives  within  a  moderate  compass  all  the  horticultural 
information  necessary  for  practical  use. — Newark  Mercury. 

A  valuable  addition  to  the  horticulturist's  library.— .Bai(imo)-e  Patriot. 

This  work  is  the  production  of  a  most  celebrated  British  horticulturist,  Dr.  Neiil,  of  Scotland,  for  up- 
wards of  thirty  years  the  Secretary  of  the  Caledonian  Horticultural  Society,  and  in  every  way  qualified  to 
make  a  standard  book  upon  the  subject  it  discusses.  The  careful  adaptation  of  the  work  to  the  peculiar 
circumstances  and  necessities  of  our  own  people,  is  a  subject  of  congratulation,  since  good  books  upon  hor- 
ticulture cannot  be  too  much  multiplied.  We  are  pleased  with  the  comprehensiveness  of  Dr.  Null's 
treatise. — Southern  Literary  Gazette. 


ELEMENTARY  PRINCIPLES  OF  CARPENTRY. 

By  Thomas  Tredgold.    In  One  Volume,  quarto,  with  nume- 
rous Illustrations  $2.50 


6 


PUBLICATIONS  OF  HENHY  CAREY  BAIRD. 


THE  ENCYCLOPEDIA  OF  CHEMISTRY,  PRACTICAL  AND 
THEORETICAL  : 

Embracing  its  Application  to  the  Arts,  Metallurgy,  Mineralogy, 

Geology,  Medicine,  and  Pharmacy.  By  James  C.  Booth,  Melter  and  Refiner  in 
the  United  States  Mint,  Professor  of  Applied  Chemistry  in  the  Franklin  Institute, 
&c. ;  assisted  by  Campbell  Morfit,  Author  of  "Chemical  Manipulations,"  &c. 
Complete  in  One  Volume,  royal  octavo,  978  pages,  with  numerous  Woodcuts  and 
other  Illustrations.    Second  Edition.    Full  bound  $5 

Tt  covers  the  whole  field  of  Chemistry  os  applied  to  Arts  and  Sciences.  *  *  *  As  no  library  is  complete 
•without  a  common  dictionary,  it  is  also  our  opinion  that  none  can  be  without  this  Encyclopedia  of  Chemis- 
try.— Scipnlijlc  Amerii-nn. 

A  work  of  time  and  labour,  and  a  treasury  of  ohemieal  information. — JVorth  American. 

By  far  the  best  manual  of  the  kind  which  has  been  presented  to  the  American  public. — Boston  Courier, 

An  invaluable  work  for  the  dissemination  of  sound  practical  knowledge. — L^'dr/cr. 

A  treasury  of  chemical  information,  including  all  the  latest  and  most  important  discoveries. — Baltimore 
American, 

At  the  first  glance  at  this  massive  volume,  one  is  amazed  at  the  amount  of  reading  furnished  in  its 
compact  double  pages,  ahout  one  thousand  in  number.  A  further  examination  shows  that  every  page  is 
richly  stored  with  information,  and  that  while  the  labours  of  the  authors  have  covered  a  wide  lield,  they 
have  neglected  or  slighted  nothing.  Every  chemical  term,  substance,  and  process  is  elaborately,  but  in- 
telligibly, described.  The  whole  science  of  Chemistry  is  placed  before  the  reader  as  fully  as  is  practicable 
with  a  science  continually  progressing.  *  *  *  Unlike  most  American  works  of  this  class,  the  authors  have 
not  depended  upon  any  one  European  work  for  their  materials.  They  have  gathered  theirs  from  works  on 
Chemistry  in  all  languages,  and  in  all  parts  of  Europe  and  America;  their  own  experience,  as  practical 
chemists,  being  ever  ready  to  settle  doubts  or  reconcile  conflicting  authorities.  The  fruit  of  so  much  toil  is 
a  work  that  must  ever  be  an  honour  to  American  science. — Evening  BuUelin. 


SYLLABUS  OF  A  COMPLETE  COURSE  OF  LECTURES  ON 
CHEMISTRY : 

Including  its  Application  to  the  Arts,  Agriculture,  and  Mining, 

prepared  for  the  use  of  the  Gentlemen  Cadets  at  the  Hon.  E.  I.  Co.'s  Military 
Seminary,  Addiscombe.  By  Professor  E.  Solly,  Lecturer  on  Chemistry  in  the 
Hon.  E.  I.  Co.'s  Military  Seminary.  Revised  by  the  Author  of  "  Chemical  Manipu- 
lations."   In  One  Volume,  octavo,  cloth  $1.25 

The  present  work  is  designed  to  occupy  a  vacant  place  in  the  libraries  of  Chemical  text-books.  It  is 
aflmirably  adapted  to  the  wants  of  both  teacher  and  pupil;  and  will  be  found  especially  convenient  to  the 
latter,  either  as  a  companion  in  the  cla.ss-room.  or  as  a  remembrancer  in  the  study.  It  gives,  at  a  glance, 
under  appropriate  headings,  a  classified  view  of  the  whole  science,  which  is  at  tlie  same  time  compendious 
and  minutely  accurate;  and  its  wide  margins  afford  sufficient  blank  space  for  such  manuscript  notes  as  the 
student  may  wish  to  add  during  lectures  or  recitations. 

The  almost  indispensable  advantages  of  such  an  impressive  aid  to  memory  are  evident  to  every  student 
who  has  used  one  in  other  branches  of  study.  Theiefore,  as  there  is  now  no  Chemical  Syllabus,  we  have 
been  induced  by  the  excellences  of  this  work  to  recommend  its  republication  in  this  country;  confident 
that  an  I'xamination  of  the  contents  will  produce  full  conviction  of  its  intrinsic  worth  and  usefulness. — 
EdiUir's  Preface, 


AN  ELEMENTARY  COURSE  OF  INSTRUCTION  ON  ORDNANCE  AND 

GUNNERY. 

Prepared  for  the  use  of  the  Midshipmen  at  the  Naval  School. 

By  James  H.  Wakd,  U.  S.  N.    In  One  Volume,  octavo  $1.50 


STEAM  FOR  THE  MILLION. 

Vn  Elementary  Outline  Treatise  on  the  Nature  and  Manage- 
ment of  steam,  and  the  Principles  and  Arrangement  of  the  Engine.  Adapted  for 
Popular  Instruction,  for  Apprentices,  and  for  the  use  of  the  Navigator.  With  an 
Appendix  containing  Notes  on  Expansive  Steam,  &c.    In  One  Volume,  8vo...37J  cts. 


PUBLICATIONS  OF  HENRY  CAREY  BAIRD. 


7 


HOUSEHOLD  SURGERY ;  OR,  HINTS  ON  EMERGENCIES. 

By  J.  F.  South,  one  of  the  Surgeons  of  St.  Thomas's  Hospi- 
tal.   In  One  Volume,  12mo.    Illustrated  by  nearly  fifty  Engravings  §1.25 

CONTENTS : 

The  Doctor's  Shop. — Poultices,  Fomentations,  Lotions,  Liniments,  Ointments,  Plasters. 

Surgery. — Blood-letting,  Blistering,  Vaccination,  Tooth-drawing,  How  to  put  on  a 
Roller,  Lancing  the  Gums,  Swollen  Veins,  Bruises,  Wounds,  Torn  or  Cut  Achilles  Ten- 
don, What  is  to  be  done  in  cases  of  sudden  Bleeding  from  various  causes,  Scalds  and 
Burns,  Frost-bite,  Chilblains,  Sprains,  Broken  Bones,  Bent  Bones,  Dislocations,  Rup- 
tures, Piles,  Protruding  Bowels,  AVetting  the  Bed,  Whitlow,  Boils,  Black-heads,  In- 
growing Nails,  Bunions,  Corns,  Sty  in  the  Eye,  Blight  in  the  Eye,  Tumours  in  the 
Eyelids,  Inflammation  on  the  Surface  of  the  Eye,  Pustules  on  the  Eye,  Milk  Abscesses, 
Sore  Nipples,  Irritable  Breast,  Breathing,  Stifling,  Choking,  Things  in  the  Eye,  On 
Dress,  Exercise  and  Diet  of  Children,  Bathing,  Infections,  Observations  on  Ventilation. 


HOUSEHOLD  MEDICINE. 

By  D.  Francis  Condie,  M.  D.   In  One  Volume,  12mo.  Uni- 
form with,  and  a  companion  to,  the  above.    (In  immediate  preparation.) 


ELWOOD'S  GRAIN  TABLES : 

Showing  the  value  of  Bushels  and  Pounds  of  different  kinds 

of  Grain,  calculated  in  Federal  Money,  so  arranged  as  to  exhibit  upon  a  single 
page  the  value  at  a  given  price  from  ten  cents  to  two  dollars  per  bushel,  of  any 
quantity  from  one  pound  to  ten  thousand  bushels.  By  J.  L.  Elwood.  A  new  Edition. 
In  One  Volume,  12mo   Si 

To  Millers  and  Produce  Dealers  this  work  is  pronounced  hy  all  who  have  it  in  use,  to  be  superior  in  ar- 
rangement to  any  work  of  the  kind  published — and  unerring  accuracy  in  every  calculation  may  be  relied 
upon  in  every  instance. 

[[y  A  reward  of  Twenty-five  Dollars  ;s  offered  for  an  error  of  one  cent  found  in  the  work. 


PERFUMERY ;  ITS  MANUFACTURE  AND  USE : 
With  Instructions  in  every  branch  of  the  Art,  and  Receipts 

for  all  the  Fashionable  Preparations ;  the  whole  forming  a  valuable  aid  to  the 
Perfumer,  Druggist,  and  Soap  Manufacturer.  Illustrated  by  numerous  AVoodcuts. 
From  the  French  of  Celnart,  and  other  late  authorities.  With  Additions  and  Im- 
provements, by  Campbell  Moefit,  one  of  the  Editors  of  the  "Encyclopedia  of 
Chemistry."    In  One  Volume,  12mo,  cloth  $1 


ELECTROTYPE  MANIPULATION: 

Being  the  Theory  and  Plain  Instructions  in  the  Art  of  "Work- 
ing in  Metals,  by  Precipitating  them  from  their  Solutions,  through  the  agency  of 
Galvanic  or  Voltaic  Electricity.  By  Chaelf.s  V.  AValkee,  Hon.  Secretary  to  the 
London  Electrical  Society,  &c.  Illustrated  by  Woodcuts.  From  the  Thirteenth 
London  Edition.    In  One  Volume,  24mo,  cloth  62  cts. 


8 


PUBLICATIONS  OF  HENRY  CAREY  BAIRD. 


PHOTOGENIC  MANIPULATION: 

Containing  the  Theory  and  Plain  Instructions  in  the  Art  of 

Photography,  or  the  Production  of  Pictures  through  the  Agency  of  Light ;  in- 
cluding Calotype,  Chrysotype,  Cyanotype,  Chromatype,  Energiatype,  Anthotype, 
Amphitype,  Daguerreotype,  Thermography,  Electrical  and  Galvanic  Impressions. 
By  George  Thomas  Fisher,  Jr.,  Assistant  in  the  Laboratory  of  the  London  In- 
stitution.   Illustrated  by  Wood-cuts.    In  One  Volume,  24mo,  cloth  62  cts. 


MATHEMATICS  FOR  PRACTICAL  MEN: 

Being  a  Common-Place  Book  of  Principles,  Theorems,  Rules, 

and  Tables,  in  various  Departments  of  Pure  and  Mixed  Mathematics,  with  their 
Applications,  especially  to  the  pursuits  of  Surveyors,  Architects,  Mechanics,  and 
Civil  Engineers.  With  numerous  Engravings.  By  Olinthus  Gregory,  L.  L.  D., 
F.  R.  A.  S  $1.50 

Only  let  men  awake,  and  fix  their  eye,  one  while  on  the  nature  of  things,  another  whOe  on  the  application 
of  them  to  the  use  and  service  of  mankind. — Lord  Bacon. 


SHEEP  HUSBANDRY  IN  THE  SOUTH : 

Comprising  a  Treatise  on  the  Acclimation  of  Sheep  in  the 

Southern  States,  and  an  Account  of  the  different  Breeds.  Also,  a  Complete  Ma- 
nual of  Breeding,  Summer  and  Winter  Management,  and  of  the  Treatment  of 
Diseases.  With  Portraits  and  other  Illustrations.  By  Henry  S.  Randall.  In 
One  Volume,  octavo  $1.25 


MISS  LESLIE'S  COMPLETE  COOKERY. 

Directions  for  Cookery,  in  its  Various  Branches.   By  Miss 

Leslie.     Forty-first  Edition.     Thorouglily  Revised,  with  the  Addition  of  New 

Receipts.    In  One  Volume,  12mo,  half  bound,  or  in  sheep  $1 

In  preparing  a  new  and  carefully  revised  edition  of  this  my  first  work  on  cookery,  I  have  introduced 
improvements,  corrected  errors,  and  added  new  receipts,  that  I  trust  will  on  trial  be  found  satisfactory.  The 
success  of  the  hook  (proved  by  its  immense  and  increasing  circulation)  affords  conclusive  evidence  that  it 
has  ol)tained  the  approbation  of  a  large  number  of  my  countrywomen;  many  of  whom  have  informed  me 
that  it  has  made  practical  housewives  of  young  ladies  who  have  entered  into  married  life  with  no  other  ac- 
quirements than  a  few  showy  accomplishments.  Gentlemen,  also,  have  told  me  of  great  improvements  in 
the  family  table,  after  presenting  their  wives  with  this  manual  of  domestic  cookery,  and  that,  after  a  morn- 
ing devoted  to  the  fatigues  of  business,  they  no  longer  find  themselves  subjected  to  the  annoyance  of  an 
ill-dressed  dinner. — Preface. 


MISS  LESLIE'S  TWO  HUNDRED  RECEIPTS  IN  FRENCH  COOKERY. 

A  new  Edition,  in  cloth  25. cts. 


TWO  HUNDRED  DESIGNS  FOR  COTTAGES  AND  VILLAS,  &c.  &c., 

Original  and  Selected.    By  Thomas  U.  Walter,  Architect  of 

Girard  College,  and  John  Jay  Smith,  Librarian  of  the  Philadelphia  Library.  In 
Four  Parts,  quarto  $10 


PUBLICATIONS  OF  HENRY  CAREY  BAIRD. 


9 


STANDARD  ILLUSTRATED  POETRY. 


THE  TALES  AND  POEMS  OF  LORD  BYRON: 

Illustrated  by  Henry  Warren.    In  One  Volume,  royal  8vo, 

with  10  Plates,  scarlet  cloth,  gilt  edges  $5 

Morocco  extra  $7 

It  is  illustrated  by  several  elegant  engravings,  from  original  designs  by  Wabren,  and  is  a  most  splendid 
work  for  the  parlour  or  study. — Boston  Evening  Gazette. 


CHILDE  HAROLD;  A  ROMAUNT  BY  LORD  BYRON: 

Illustrated  by  12  Splendid  Plates,  by  Warren  and  others.  In 

One  Volume,  royal  8vo,  cloth  extra,  gilt  edges  $5 

Morocco  extra  $7 

Printed  in  elegant  style,  with  splendid  pictures,  far  superior  to  any  thing  of  the  sort  usually  found  in 
books  of  this  kind. — iV.  T.  Courier. 


SPECIMENS  OF  THE  BRITISH  POETS. 

From  the  time  of  Chaucer  to  the  end  of  the  Eighteenth  Cen- 
tury.   By  Thomas  Campbell.    In  One  Volume,  royal  8vo.    (In  press.) 


THE  FEMALE  POETS  OF  AMERICA. 

By  KuFUS  W.  Griswold.    A  new  Edition.   In  One  Volume, 

royal  8vo.    Cloth,  gilt  $2.50 

Cloth  extra,  gilt  edges  $3 

Morocco  super  extra  $4.50 

The  best  production  which  has  yet  come  from  the  pen  of  Dr.  Griswold,  and  the  most  valuable  contribu- 
tion which  he  has  ever  made  to  the  literary  celebrity  of  the  country. — iV.  Y.  Tribune. 


THE  LADY  OF  THE  LAKE : 

By  Sir  Walter  Scott.   Illustrated  with  10  Plates,  by  Cor- 

BOULD  and  Meadows.    In  One  Volume,  royal  Svo.    Bound  in  cloth  extra,  gilt 

edges  $5 

Turkey  morocco  super  extra  $7 

This  is  one  of  the  most  truly  beautiful  books  which  has  ever  issued  firom  the  American  press. 


LALLA  ROOKH;  A  ROMANCE  BY  THOMAS  MOORE: 

Illustrated  by  13  Plates,  from  Designs  by  Corbould,  Meadows, 

and  Stephanoff.   In  One  Volume,  royal  Svo.   Bound  in  cloth  extra,  gilt  edges. ..$5 

Turkey  morocco  super  extra  $7 

This  is  published  in  a  style  uniform  with  the  •'  Lady  of  the  Lake." 


10 


PUBLICATIONS  OF  HENRY  CAHEY  BAIRD. 


THE  POETICAL  WORKS  OF  THOMAS  GRAY: 

With  Illustrations  by  C.  W.  Radcliffe,  Edited  with  a  Me- 
moir, by  Henrt  Reed,  Professor  of  English  Literature  in  the  University  of  Penn- 
sylvania.   In  One  Volume,  8vo.    Bound  in  cloth  extra,  gilt  edges  $3.50 

Turkey  morocco  super  extra  $5.50 

It  i.i  many  a  day  since  we  have  seen  issued  from  the  press  of  our  country  a  volume  so  complete  and  truly 
elegant  in  every  respect.  The  typography  is  faultless,  the  illustrations  superior,  and  the  binding  superb. — 
Troy  Whig. 

We  have  not  seen  a  specimen  of  typographical  luxury  from  the  American  press  which  can  surpass  this 
volume  in  choice  elegance. — Boston  Courier. 

It  is  eminently  calculated  to  consecrate  among  American  readers  (if  they  have  not  been  consecrated 
already  in  their  hearts)  the  pure,  the  elegant,  the  refined,  and,  in  many  respects,  the  sublime  imaginings 
of  TuoMAS  Gray. — Richmond  Whig, 


THE  POETICAL  WORKS  OF  HENRY  WADSWORTH  LONGFELLOW: 

Illustrated  by  10  Plates,  after  Designs  by  D.  Huntingdon, 

with  a  Portrait.   Ninth  Edition.    In  One  Volume,  royal  8vo.   Bound  in  cloth  extra, 

gilt  edges  $5 

Morocco  super  extra  $7 

This  is  the  very  luxury  of  literature — LoNOFELLOvr's  charming  poems  presented  in  a  form  of  unsurpassed 
beauty. — JVeaVs  Gazette. 


POETS  AND  POETRY  OF  ENGLAND  IN  THE  NINETEENTH 

CENTURY: 

By  RuFUS  W.  Griswold.    Illustrated.   In  One  Volume,  royal 

8vo.    Bound  in  cloth  $3 

Cloth  extra,  gilt  edges  $3.50 

Morocco  super  extra  $5 

Such  is  the  critical  acumen  discovered  in  these  selections,  that  scarcely  a  page  is  to  be  found  but  is  redo- 
lent with  beauties,  and  the  volume  itself  may  be  regarded  as  a  galaxy  of  literary  pearls. — Democratic 
Review. 


THE  POETS  AND  POETRY  OF  THE  ANCIENTS : 

By  "William  Peter,  A.  M.   Comprising  Translations  and  Spe- 
cimens of  the  Poets  of  Greece  and  Rome,  with  an  elegant  engraved  View  of  the 

Coliseum  at  Rome.    Bound  in  cloth  $3 

Cloth  extra,  gilt  edges  $3.50 

Turkey  morocco  super  extra  $5 


THE  FEMALE  POETS  OF  GREAT  BRITAIN. 

With  Copious  Selections  and  Critical  Remarks.    By  Frederic 

RowTON.  With  Additions  by  an  American  Editor,  and  finely  engraved  Illustra- 
tions by  celebrated  Artists.    In  One  Volume,  royal  Svo.    Bound  in  cloth  extra, 

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• 


Date  Due  ' 

1 

GETTY  CENTER  LIBRARY 


